From b904bc2994dcc0f67740e5425615b8de95651158 Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Mon, 11 Oct 2021 17:02:03 -0400 Subject: [PATCH 01/11] Handle arbitrary convex constraints in DFO-LS --- dfols/__init__.py | 3 +- dfols/controller.py | 133 +++++++++++++-- dfols/model.py | 11 +- dfols/params.py | 11 ++ dfols/solver.py | 37 ++++- dfols/tests/test_model.py | 30 ++-- dfols/tests/test_trust_region.py | 274 ++++++++++++++++++++++++++++++- dfols/trust_region.py | 159 +++++++++++++++++- dfols/util.py | 53 +++++- dfols/version.py | 2 +- 10 files changed, 668 insertions(+), 45 deletions(-) diff --git a/dfols/__init__.py b/dfols/__init__.py index 74d7e05..5ae8a0e 100644 --- a/dfols/__init__.py +++ b/dfols/__init__.py @@ -7,8 +7,7 @@ It solves the nonlinear least-squares problem: min_{x} f(x) = r1(x)**2 + ... + rm(x)**2, -subject to the (optional) bounds - lb <= x <= ub, +(optionally) subject to finitely many convex constraints, where each function ri(x) is differentiable, possibly nonconvex. Since the derivatives of ri(x) are never required or approximated, the solver works when the evaluation of ri(x) is noisy. diff --git a/dfols/controller.py b/dfols/controller.py index 0796858..5ace32c 100644 --- a/dfols/controller.py +++ b/dfols/controller.py @@ -92,13 +92,13 @@ def able_to_do_restart(self): class Controller(object): - def __init__(self, objfun, args, x0, r0, r0_nsamples, xl, xu, npt, rhobeg, rhoend, nf, nx, maxfun, params, + def __init__(self, objfun, args, x0, r0, r0_nsamples, xl, xu, projections, npt, rhobeg, rhoend, nf, nx, maxfun, params, scaling_changes, do_logging): self.do_logging = do_logging self.objfun = objfun self.args = args self.maxfun = maxfun - self.model = Model(npt, x0, r0, xl, xu, r0_nsamples, precondition=params("interpolation.precondition"), + self.model = Model(npt, x0, r0, xl, xu, projections, r0_nsamples, precondition=params("interpolation.precondition"), abs_tol = params("model.abs_tol"), rel_tol = params("model.rel_tol"), do_logging=do_logging) self.nf = nf self.nx = nx @@ -137,6 +137,107 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa assert self.model.num_pts <= (self.n() + 1) * (self.n() + 2) // 2, "prelim: must have npt <= (n+1)(n+2)/2" assert 1 <= num_directions < self.model.num_pts, "Initialisation: must have 1 <= ndirs_initial < npt" + + if self.model.projections: + D = np.zeros((self.n(),self.n())) + k = 0 + while k < self.n(): + ek = np.zeros(self.n()) + ek[k] = 1 + p = np.dot(ek,self.delta) + yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol")) + D[k,:] = yk - self.model.xbase + + k += 1 # move on to next point + + # Have at least one L.D. vector, try negative direction on bad one first + k = 0 + mr_tol = params("matrix_rank.r_tol") + D_rank, diag = qr_rank(D,tol=mr_tol) + while D_rank != num_directions and k < self.n(): + if diag[k] < mr_tol: + ek = np.zeros(self.n()) + ek[k] = 1 + p = -np.dot(ek,self.delta) + yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol")) + dk = D[k,:].copy() + D[k,:] = yk - self.model.xbase + D_rank2, _diag2 = qr_rank(D,tol=params("matrix_rank.r_tol")) + if D_rank2 <= D_rank: + # Did not improve rank, revert change + D[k,:] = dk + # rank was improved, update D_rank for next comparison + D_rank = D_rank2 + k += 1 + + # Try random combination of negatives... + k = 0 + slctr = np.random.randint(0, 1+1, self.n()) # generate rand binary "selector" array + D_rank, diag = qr_rank(D,tol=params("matrix_rank.r_tol")) + while D_rank != num_directions and k < 100*self.n(): + if slctr[k%self.n()] == 1: # if selector says make -ve, make -ve + ek = np.zeros(self.n()) + ek[k%self.n()] = 1 + p = -np.dot(ek,self.delta) + yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol")) + dk = D[k%self.n(),:].copy() + D[k%self.n(),:] = yk - self.model.xbase + D_rank2, _diag2 = qr_rank(D,tol=params("matrix_rank.r_tol")) + if D_rank2 <= D_rank: + # Did not improve rank, revert change + D[k%self.n(),:] = dk + # rank was improved, update D_rank for next comparison + D_rank = D_rank2 + + # Go again + slctr = np.random.randint(0, 1+1, self.n()) + k += 1 + + # Set still not L.I? Try random directions + i = 0 + D_rank, diag = qr_rank(D,tol=params("matrix_rank.r_tol")) + while D_rank != num_directions and i <= 100*num_directions: + k = 0 + while k < self.n(): + if diag[k] < mr_tol: + p = np.random.normal(size=self.n()) + p = p/np.linalg.norm(p) + p = np.dot(p,self.delta) + yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol")) + dk = D[k,:].copy() + D[k,:] = yk - self.model.xbase + D_rank2, _diag2 = qr_rank(D,tol=params("matrix_rank.r_tol")) + if D_rank2 <= D_rank: + # Did not improve rank, revert change + D[k,:] = dk + # rank was improved, update D_rank for next comparison + D_rank = D_rank2 + k += 1 + i += 1 + + if D_rank != num_directions: + raise RuntimeError("Unable to generate suitable initial directions") + + # we have a L.I set of interpolation points + for k in range(0,self.n()): + # Evaluate objective at this new point + x = self.model.as_absolute_coordinates(D[k, :]) + rvec_list, f_list, num_samples_run, exit_info = self.evaluate_objective(x, number_of_samples, params) + + # Handle exit conditions (f < min obj value or maxfun reached) + if exit_info is not None: + if num_samples_run > 0: + self.model.save_point(x, np.mean(rvec_list[:num_samples_run, :], axis=0), num_samples_run, + x_in_abs_coords=True) + return exit_info # return & quit + + # Otherwise, add new results (increments model.npt_so_far) + self.model.change_point(k+1, x - self.model.xbase, rvec_list[0, :]) # expect step, not absolute x + for i in range(1, num_samples_run): + self.model.add_new_sample(k+1, rvec_extra=rvec_list[i, :]) + + return None # return & continue + at_lower_boundary = (self.model.sl > -0.01 * self.delta) # sl = xl - x0, should be -ve, actually < -rhobeg at_upper_boundary = (self.model.su < 0.01 * self.delta) # su = xu - x0, should be +ve, actually > rhobeg @@ -147,17 +248,19 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa # k = 2n+1, ..., (n+1)(n+2)/2 --> off-diagonal directions if 1 <= k < self.n() + 1: # first step along coord directions dirn = k - 1 # direction to move in (0,...,n-1) - stepa = self.delta if not at_upper_boundary[dirn] else -self.delta + stepa = self.delta if not at_upper_boundary[dirn] else -self.delta # take a +delta step if at lower, -delta if at upper stepb = None - xpts_added[k, dirn] = stepa + xpts_added[k, dirn] = stepa # set new (relative) point to the step since we haven't done any moving, so relative point is all zeros. elif self.n() + 1 <= k < 2 * self.n() + 1: # second step along coord directions dirn = k - self.n() - 1 # direction to move in (0,...,n-1) - stepa = xpts_added[k - self.n(), dirn] - stepb = -self.delta + stepa = xpts_added[k - self.n(), dirn] # previous step + stepb = -self.delta # new step if at_lower_boundary[dirn]: + # if at lower boundary, set the second step to be +ve stepb = min(2.0 * self.delta, self.model.su[dirn]) # su = xu - x0, should be +ve if at_upper_boundary[dirn]: + # if at upper boundary, set the second step to be -ve stepb = max(-2.0 * self.delta, self.model.sl[dirn]) # sl = xl - x0, should be -ve xpts_added[k, dirn] = stepb @@ -325,10 +428,13 @@ def get_new_direction_for_growing(self, step_length): return dirn * (step_length / LA.norm(dirn)) - def trust_region_step(self): + def trust_region_step(self, params): # Build model for full least squares objectives gopt, H = self.model.build_full_model() - d, gnew, crvmin = trsbox(self.model.xopt(), gopt, H, self.model.sl, self.model.su, self.delta) + if self.model.projections: + d, gnew, crvmin = ctrsbox(self.model.xopt(abs_coordinates=True), gopt, H, self.model.projections, self.delta, d_max_iters=params("dykstra.max_iters"), d_tol=params("dykstra.d_tol")) + else: + d, gnew, crvmin = trsbox(self.model.xopt(), gopt, H, self.model.sl, self.model.su, self.delta) return d, gopt, H, gnew, crvmin def geometry_step(self, knew, adelt, number_of_samples, params): @@ -337,8 +443,13 @@ def geometry_step(self, knew, adelt, number_of_samples, params): try: c, g = self.model.lagrange_gradient(knew) # c = 1.0 if knew == self.model.kopt else 0.0 # based at xopt, just like d - # Solve problem: bounds are sl <= xnew <= su, and ||xnew-xopt|| <= adelt - xnew = trsbox_geometry(self.model.xopt(), c, g, np.minimum(self.model.sl, 0.0), np.maximum(self.model.su, 0.0), adelt) + if self.model.projections: + # Solve problem: use projection onto arbitrary constraints, and ||xnew-xopt|| <= adelt + step = ctrsbox_geometry(self.model.xopt(abs_coordinates=True), c, g, self.model.projections, adelt, d_max_iters=params("dykstra.max_iters"), d_tol=params("dykstra.d_tol")) + xnew = self.model.xopt() + step + else: + # Solve problem: bounds are sl <= xnew <= su, and ||xnew-xopt|| <= adelt + xnew = trsbox_geometry(self.model.xopt(), c, g, np.minimum(self.model.sl, 0.0), np.maximum(self.model.su, 0.0), adelt) except LA.LinAlgError: exit_info = ExitInformation(EXIT_LINALG_ERROR, "Singular matrix encountered in geometry step") return exit_info # didn't fix geometry - return & quit @@ -499,7 +610,7 @@ def reduce_rho(self, current_iter, params): def calculate_ratio(self, current_iter, rvec_list, d, gopt, H): exit_info = None f = sumsq(np.mean(rvec_list, axis=0)) # estimate actual objective value - pred_reduction = - model_value(gopt, H, d) + pred_reduction = - model_value(gopt, H, d) # negative of m since m(0) = 0 actual_reduction = self.model.fopt() - f self.diffs = [abs(actual_reduction - pred_reduction), self.diffs[0], self.diffs[1]] if min(sqrt(sumsq(d)), self.delta) > self.rho: # if ||d|| >= rho, successful! diff --git a/dfols/model.py b/dfols/model.py index 20373a9..745f2e6 100644 --- a/dfols/model.py +++ b/dfols/model.py @@ -36,12 +36,12 @@ import scipy.linalg as LA from .trust_region import trsbox_geometry -from .util import sumsq +from .util import sumsq, dykstra __all__ = ['Model'] class Model(object): - def __init__(self, npt, x0, r0, xl, xu, r0_nsamples, n=None, m=None, abs_tol=1e-12, rel_tol=1e-20, precondition=True, + def __init__(self, npt, x0, r0, xl, xu, projections, r0_nsamples, n=None, m=None, abs_tol=1e-12, rel_tol=1e-20, precondition=True, do_logging=True): if n is None: n = len(x0) @@ -63,6 +63,7 @@ def __init__(self, npt, x0, r0, xl, xu, r0_nsamples, n=None, m=None, abs_tol=1e- self.xbase = x0.copy() self.sl = xl - self.xbase # lower bound w.r.t. xbase (require xpt >= sl) self.su = xu - self.xbase # upper bound w.r.t. xbase (require xpt <= su) + self.projections = projections self.points = np.zeros((npt, n)) # interpolation points w.r.t. xbase # Function values @@ -123,6 +124,8 @@ def xpt(self, k, abs_coordinates=False): return np.minimum(np.maximum(self.sl, self.points[k, :].copy()), self.su) else: # Apply bounds and convert back to absolute coordinates + if self.projections: + return dykstra(self.projections, self.xbase + self.points[k,:]) return self.xbase + np.minimum(np.maximum(self.sl, self.points[k, :]), self.su) def rvec(self, k): @@ -133,8 +136,10 @@ def fval(self, k): assert 0 <= k < self.npt(), "Invalid index %g" % k return self.fval[k] - def as_absolute_coordinates(self, x): + def as_absolute_coordinates(self, x, full_dykstra=False): # If x were an interpolation point, get the absolute coordinates of x + if self.projections: + return dykstra(self.projections, self.xbase + x) return self.xbase + np.minimum(np.maximum(self.sl, x), self.su) def xpt_directions(self, include_kopt=True): diff --git a/dfols/params.py b/dfols/params.py index e3e2622..e168c01 100644 --- a/dfols/params.py +++ b/dfols/params.py @@ -109,6 +109,11 @@ def __init__(self, n, npt, maxfun, objfun_has_noise=False): self.params["growing.full_rank.min_sing_val"] = 1e-6 # absolute floor on singular values self.params["growing.full_rank.svd_max_jac_cond"] = 1e8 # maximum condition number of Jacobian self.params["growing.perturb_trust_region_step"] = False # add random direction onto TRS solution? + # Dykstra's algorithm + self.params["dykstra.d_tol"] = 1e-10 + self.params["dykstra.max_iters"] = 100 + # Matrix rank algorithm + self.params["matrix_rank.r_tol"] = 1e-16 self.params_changed = {} for p in self.params: @@ -257,6 +262,12 @@ def param_type(self, key, npt): type_str, nonetype_ok, lower, upper = 'float', True, 1.0, None elif key == "growing.perturb_trust_region_step": type_str, nonetype_ok, lower, upper = 'bool', False, None, None + elif key == "dykstra.d_tol": + type_str, nonetype_ok, lower, upper = 'float', False, 0.0, None + elif key == "dykstra.max_iters": + type_str, nonetype_ok, lower, upper = 'int', False, 0, None + elif key == "matrix_rank.r_tol": + type_str, nonetype_ok, lower, upper = 'float', False, 0.0, None else: assert False, "ParameterList.param_type() has unknown key: %s" % key return type_str, nonetype_ok, lower, upper diff --git a/dfols/solver.py b/dfols/solver.py index f6279ba..cb487ef 100644 --- a/dfols/solver.py +++ b/dfols/solver.py @@ -93,7 +93,7 @@ def __str__(self): return output -def solve_main(objfun, x0, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns_so_far, nf_so_far, nx_so_far, nsamples, params, +def solve_main(objfun, x0, args, xl, xu, projections, npt, rhobeg, rhoend, maxfun, nruns_so_far, nf_so_far, nx_so_far, nsamples, params, diagnostic_info, scaling_changes, r0_avg_old=None, r0_nsamples_old=None, default_growing_method_set_by_user=None, do_logging=True, print_progress=False): # Evaluate at x0 (keep nf, nx correct and check for f < 1e-12) @@ -160,7 +160,7 @@ def solve_main(objfun, x0, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns_so_f params('growing.delta_scale_new_dirns', new_value=0.1) # Initialise controller - control = Controller(objfun, args, x0, r0_avg, num_samples_run, xl, xu, npt, rhobeg, rhoend, nf, nx, maxfun, + control = Controller(objfun, args, x0, r0_avg, num_samples_run, xl, xu, projections, npt, rhobeg, rhoend, nf, nx, maxfun, params, scaling_changes, do_logging) # Initialise interpolation set @@ -271,7 +271,7 @@ def solve_main(objfun, x0, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns_so_f # Trust region step - d, gopt, H, gnew, crvmin = control.trust_region_step() + d, gopt, H, gnew, crvmin = control.trust_region_step(params) if do_logging: logging.debug("Trust region step is d = " + str(d)) xnew = control.model.xopt() + d @@ -851,7 +851,7 @@ def solve_main(objfun, x0, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns_so_f return x, rvec, f, jacmin, nsamples, control.nf, control.nx, nruns_so_far, exit_info, diagnostic_info -def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, maxfun=None, nsamples=None, user_params=None, +def solve(objfun, x0, args=(), bounds=None, projections=[], npt=None, rhobeg=None, rhoend=1e-8, maxfun=None, nsamples=None, user_params=None, objfun_has_noise=False, scaling_within_bounds=False, do_logging=True, print_progress=False): x0 = x0.astype(float) n = len(x0) @@ -869,6 +869,10 @@ def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, scaling_within_bounds = False warnings.warn("Ignoring scaling_within_bounds=True for unconstrained problem/1-sided bounds", RuntimeWarning) + if projections and scaling_within_bounds: + scaling_within_bounds = False + warnings.warn("Ignoring scaling_within_bounds=True for black-box constrained problem", RuntimeWarning) + if xl is None: xl = -1e20 * np.ones((n,)) # unconstrained if xu is None: @@ -882,6 +886,18 @@ def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, if nsamples is None: nsamples = lambda delta, rho, iter, nruns: 1 # no averaging + # If using arbitrary constraints, create projection from bounds + if projections: + xlb = xl.copy() + xub = xu.copy() + bproj = lambda w: pbox(w,xlb,xub) + projections = projections.copy() + projections.append(bproj) + + # since using arbitrary constraints, don't constrain otherwise + xl = -1e20 * np.ones((n,)) + xu = 1e20 * np.ones((n,)) + # Set parameters params = ParameterList(int(n), int(npt), int(maxfun), objfun_has_noise=objfun_has_noise) # make sure int, not np.int if user_params is not None: @@ -976,6 +992,13 @@ def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, results = OptimResults(None, None, None, None, 0, 0, 0, exit_flag, exit_msg) return results + # Enforce arbitrary constraint bounds on x0 + if projections: + xp = dykstra(projections,x0,max_iter=params("dykstra.max_iters"),tol=params("dykstra.d_tol")) + if not np.allclose(xp,x0): + warnings.warn("x0 not feasible w.r.t given constraints, adjusting", RuntimeWarning) + x0 = xp.copy() + # Enforce lower & upper bounds on x0 idx = (x0 <= xl) if np.any(idx): @@ -993,7 +1016,7 @@ def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, nf = 0 nx = 0 xmin, rmin, fmin, jacmin, nsamples_min, nf, nx, nruns, exit_info, diagnostic_info = \ - solve_main(objfun, x0, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, + solve_main(objfun, x0, args, xl, xu, projections, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, diagnostic_info, scaling_changes, default_growing_method_set_by_user=default_growing_method_set_by_user, do_logging=do_logging, print_progress=print_progress) @@ -1012,12 +1035,12 @@ def solve(objfun, x0, args=(), bounds=None, npt=None, rhobeg=None, rhoend=1e-8, % (fmin, nf, rhobeg, rhoend)) if params("restarts.hard.use_old_rk"): xmin2, rmin2, fmin2, jacmin2, nsamples2, nf, nx, nruns, exit_info, diagnostic_info = \ - solve_main(objfun, xmin, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, + solve_main(objfun, xmin, args, xl, xu, projections, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, diagnostic_info, scaling_changes, r0_avg_old=rmin, r0_nsamples_old=nsamples_min, do_logging=do_logging, print_progress=print_progress) else: xmin2, rmin2, fmin2, jacmin2, nsamples2, nf, nx, nruns, exit_info, diagnostic_info = \ - solve_main(objfun, xmin, args, xl, xu, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, + solve_main(objfun, xmin, args, xl, xu, projections, npt, rhobeg, rhoend, maxfun, nruns, nf, nx, nsamples, params, diagnostic_info, scaling_changes, do_logging=do_logging, print_progress=print_progress) if fmin2 < fmin or np.isnan(fmin): diff --git a/dfols/tests/test_model.py b/dfols/tests/test_model.py index 9b6a384..66ed89f 100644 --- a/dfols/tests/test_model.py +++ b/dfols/tests/test_model.py @@ -46,7 +46,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e20 * np.ones((n,)) xu = 1e20 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) self.assertEqual(model.npt(), 1, 'Wrong npt after initialisation') self.assertTrue(array_compare(model.xopt(abs_coordinates=True), x0), 'Wrong xopt after initialisation') self.assertTrue(array_compare(model.ropt(), rosenbrock(x0)), 'Wrong ropt after initialisation') @@ -97,7 +97,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e20 * np.ones((n,)) xu = 1e20 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) # Now add better point x1 = np.array([1.0, 0.9]) rvec = rosenbrock(x1) @@ -124,7 +124,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) self.assertTrue(array_compare(model.sl, xl - x0), 'Wrong sl after initialisation') self.assertTrue(array_compare(model.su, xu - x0), 'Wrong su after initialisation') x1 = np.array([1.0, 0.9]) @@ -204,7 +204,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) x1 = np.array([1.0, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) x2 = np.array([1.0, 1.0]) @@ -224,17 +224,17 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) x1 = np.array([1.0, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) x2 = np.array([2.0, 0.9]) model.change_point(2, x2 - model.xbase, rosenbrock(x2)) self.assertAlmostEqual(model.min_objective_value(), 1e-12, 'Wrong min obj value') - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1, rel_tol=1e-2) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1, rel_tol=1e-2) self.assertAlmostEqual(model.min_objective_value(), 1e-2 * sumsq(rosenbrock(x0)), 'Wrong min obj value 2') - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1, abs_tol=1.0) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1, abs_tol=1.0) self.assertAlmostEqual(model.min_objective_value(), 1.0, 'Wrong min obj value 3') - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1, abs_tol=1.0, rel_tol=1e-2) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1, abs_tol=1.0, rel_tol=1e-2) self.assertAlmostEqual(model.min_objective_value(), 1.0, 'Wrong min obj value 4') @@ -245,7 +245,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) model.add_new_sample(0, rosenbrock(x0)) x1 = np.array([1.0, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) @@ -295,7 +295,7 @@ def runTest(self): # x0 = np.array([1.0, 2.9]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) model.add_new_sample(0, rosenbrock(x0)) x1 = np.array([1.0, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) @@ -326,7 +326,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) model.add_new_sample(0, rosenbrock(x0)) x1 = np.array([-1.2, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) @@ -354,7 +354,7 @@ def runTest(self): delta = 0.5 xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) model.add_new_sample(0, rosenbrock(x0)) x1 = x0 + delta * np.array([1.0, 0.0]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) @@ -373,7 +373,7 @@ def runTest(self): x0 = np.array([-1.2, 1.0]) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, x0, rosenbrock(x0), xl, xu, 1) + model = Model(npt, x0, rosenbrock(x0), xl, xu, [], 1) x1 = np.array([1.0, 0.9]) model.change_point(1, x1 - model.xbase, rosenbrock(x1)) x2 = np.array([2.0, 0.9]) @@ -407,7 +407,7 @@ def runTest(self): # x0 = np.zeros((n,)) xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) - model = Model(npt, A[0,:], np.array([b[0]]), xl, xu, 1) + model = Model(npt, A[0,:], np.array([b[0]]), xl, xu, [], 1) for i in range(1,npt): xi = A[i,:] @@ -450,7 +450,7 @@ def runTest(self): xl = -1e2 * np.ones((n,)) xu = 1e2 * np.ones((n,)) # model = Model(n+1, x0, np.array([0.0]), xl, xu, 1) - model = Model(n+1, A[0, :], np.array([b[0]]), xl, xu, 1) + model = Model(n+1, A[0, :], np.array([b[0]]), xl, xu, [], 1) for i in range(1,npt): xi = A[i,:] diff --git a/dfols/tests/test_trust_region.py b/dfols/tests/test_trust_region.py index 64524e3..840d1f1 100644 --- a/dfols/tests/test_trust_region.py +++ b/dfols/tests/test_trust_region.py @@ -27,7 +27,7 @@ import numpy as np import unittest -from dfols.trust_region import trsbox, trsbox_geometry +from dfols.trust_region import ctrsbox, ctrsbox_geometry, trsbox, trsbox_geometry from dfols.util import model_value @@ -70,6 +70,171 @@ def cauchy_pt_box(g, H, delta, lower, upper): crvmin = -1.0 return s, red, crvmin +def p_box(x,l,u): + return np.minimum(np.maximum(x,l), u) + +class TestUncInternalCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 2.0 + xopt = np.ones((n,)) # trying nonzero (since bounds inactive) + sl = -1e20 * np.ones((n,)) + su = 1e20 * np.ones((n,)) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([-1.0, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer for internal minimum? + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') + print(crvmin) + self.assertAlmostEqual(crvmin, 1.2, 'Wrong crvmin') + +class TestUncBdryCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + sl = -1e20 * np.ones((n,)) + su = 1e20 * np.ones((n,)) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') + self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') + +class TestUncBdry2CDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + sl = -1e20 * np.ones((n,)) + su = 1e20 * np.ones((n,)) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.allclose(gnew, g + H.dot(d)), 'Wrong gnew') + self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') + +class TestUncBdry3CDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([0.0, 0.0, 1.0]) + H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) + Delta = 0.5 + xopt = np.zeros((n,)) + sl = -1e20 * np.ones((n,)) + su = 1e20 * np.ones((n,)) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([0.0, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') + self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') + # self.assertAlmostEqual(crvmin, crvmin_cauchy, 'Wrong crvmin') + +class TestUncHardCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([0.0, 0.0, 1.0]) + H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) + Delta = sqrt(2.0) + xopt = np.zeros((n,)) + sl = -1e20 * np.ones((n,)) + su = 1e20 * np.ones((n,)) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([1.0, 0.0, -1.0]) # non-unique solution + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') + self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') + +class TestConInternalCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 2.0 + xopt = np.ones((n,)) # trying nonzero (since bounds inactive) + sl = xopt + np.array([-0.5, -10.0, -10.0]) + su = xopt + np.array([10.0, 10.0, 10.0]) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([-1.0, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer for internal minimum? + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl-xopt, su-xopt) + # print(s_cauchy) + # print(d) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') + print(crvmin) + self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin') + + +# Notes: Gets correct min and gnew. Incorrect crvmin (1.0999999999999999). +class TestConBdryCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + sl = xopt + np.array([-0.3, -0.01, -0.1]) + su = xopt + np.array([10.0, 1.0, 10.0]) + pbox = lambda x: p_box(x,sl,su) + d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) + true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + # Hope to get actual correct answer + # self.assertTrue(np.all(d == true_d), 'Wrong answer') + # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') + s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl - xopt, su - xopt) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.max(np.abs(gnew - g - H.dot(d))) < 1e-10, 'Wrong gnew') + print(crvmin) + self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin') + # self.assertAlmostEqual(crvmin, crvmin_cauchy, 'Wrong crvmin') + class TestUncInternal(unittest.TestCase): def runTest(self): @@ -340,3 +505,110 @@ def runTest(self): # print(x) # print(xtrue) self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeomCDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([1.0, -1.0]) + a = np.array([-2.0, -2.0]) + b = np.array([1.0, 2.0]) + delta = 2.0 + c = -1.0 + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([-sqrt(2.0), sqrt(2.0)]) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeom2CDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([1.0, -1.0]) + a = np.array([-2.0, -2.0]) + b = np.array([1.0, 2.0]) + delta = 5.0 + c = -1.0 + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([-2.0, 2.0]) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeom3CDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + 1 + g = np.array([1.0, -1.0]) + a = np.array([-2.0, -2.0]) + 1 + b = np.array([1.0, 2.0]) + 1 + delta = 5.0 + c = 3.0 # may want to max instead + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([1.0, -2.0]) + 1 + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeomOldBugCDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([-1.0, -1.0]) + a = np.array([-2.0, -2.0]) + b = np.array([0.1, 0.9]) + delta = sqrt(2.0) + c = -1.0 # may want to max instead + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = b + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + # self.assertFalse(True, "bad") + + +class TestGeomOldBug2CDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0, 0.0]) + g = np.array([-1.0, -1.0, -1.0]) + a = np.array([-2.0, -2.0, -2.0]) + b = np.array([0.9, 0.1, 5.0]) + delta = sqrt(3.0) + c = -1.0 # may want to max instead + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([0.9, 0.1, sqrt(3.0 - 0.81 - 0.01)]) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + # self.assertFalse(True, "bad") + +class TestGeom2WithZerosCDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([0.0, -1.0]) + a = np.array([-2.0, -2.0]) + b = np.array([1.0, 2.0]) + delta = 5.0 + c = 0.0 + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([0.0, 2.0]) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeom2WithAlmostZerosCDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([1e-15, -1.0]) + a = np.array([-2.0, -2.0]) + b = np.array([1.0, 2.0]) + delta = 5.0 + c = 0.0 + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([0.0, 2.0]) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + + +class TestGeom2WithAlmostZeros2CDFO(unittest.TestCase): + def runTest(self): + xbase = np.array([0.0, 0.0]) + g = np.array([1e-15, 0.0]) + a = np.array([-2.0, -2.0]) + b = np.array([1.0, 2.0]) + delta = 5.0 + c = 0.0 + x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) + xtrue = np.array([0.0, 0.0]) + # print(x) + # print(xtrue) + self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') diff --git a/dfols/trust_region.py b/dfols/trust_region.py index ec8c975..8b0a21d 100644 --- a/dfols/trust_region.py +++ b/dfols/trust_region.py @@ -11,6 +11,15 @@ The other outputs: gnew is the gradient of the model at d, and crvmin has information about the curvature of the model at the solution. +For handling arbitrary constraints, the call is + d, gnew, crvmin = ctrsbox(xopt, g, H, projections, delta) +which produces a new vector d approximately solving the constrained trust region subproblem: + min_{d} g'*d + 0.5*d'*H*d + s.t. ||d|| <= delta + xopt + d is feasible w.r.t. the constraint set C +The other outputs: gnew is the gradient of the model at d, and crvmin has +information about the curvature of the model at the solution. + We also provide a function for maximising the absolute value of a linear function inside a similar trust region - this is useful for geometry steps. The call @@ -23,6 +32,13 @@ min_s abs(c + g' * d) s.t. lower <= xbase + d <= upper ||d|| <= delta +Again, we have a version of this for handling arbitrary constraints +The call + x = ctrsbox_geometry(xbase, c, g, projections, Delta) +Solves + min_s abs(c + g' * d) + s.t. xbase + d is feasible w.r.t. the constraint set C + ||d|| <= delta Notes ---- @@ -63,13 +79,77 @@ # Fall back to Python implementation USE_FORTRAN = False +from .util import dykstra, pball, pbox, sumsq, model_value -from .util import sumsq +__all__ = ['ctrsbox', 'ctrsbox_geometry', 'trsbox', 'trsbox_geometry'] +ZERO_THRESH = 1e-14 -__all__ = ['trsbox', 'trsbox_geometry'] +def ctrsbox(xopt, g, H, projections, delta, d_max_iters=100, d_tol=1e-10, use_fortran=USE_FORTRAN): + n = xopt.size + assert xopt.shape == (n,), "xopt has wrong shape (should be vector)" + assert g.shape == (n,), "g and xopt have incompatible sizes" + assert len(H.shape) == 2, "H must be a matrix" + assert H.shape == (n,n), "H and xopt have incompatible sizes" + assert np.allclose(H, H.T), "H must be symmetric" + assert delta > 0.0, "delta must be strictly positive" -ZERO_THRESH = 1e-14 + d = np.zeros((n,)) + gnew = g.copy() + gy = g.copy() + crvmin = -1.0 + y = d.copy() + eta = 1.2 # L backtrack scaling factor + t = 1 + + # Initial guess of L is norm(Hessian) + L = np.linalg.norm(H, 2) + + # trust region is a ball of radius delta around xopt + trproj = lambda w: pball(w, xopt, delta) + + # combine trust region constraints with user-entered constraints + P = projections.copy() + P.append(trproj) + def proj(d0): + p = dykstra(P, xopt+d0, max_iter=d_max_iters, tol=d_tol) + # we want the step only, so we subtract xopt + # from the new point: proj(xk+d) - xk + return p - xopt + + MAX_LOOP_ITERS = 100 * n ** 2 + + # projected GD loop + for ii in range(MAX_LOOP_ITERS): + w = y - (1/L)*gy + prev_d = d.copy() + d = proj(w) + + # size of step taken + s = d - prev_d + stplen = np.linalg.norm(s) + + # update true gradient + gnew += H.dot(s) + + # update CRVMIN + crv = s.dot(H).dot(s)/sumsq(s) + crvmin = min(crvmin, crv) if crvmin != -1.0 else crv + + # exit condition + if stplen <= ZERO_THRESH: + break + + # momentum update + prev_t = t + t = (1 + np.sqrt(1 + 4 * t ** 2))/2 + prev_y = y.copy() + y = d + s*(prev_t - 1)/t + + # update gradient w.r.t y + gy += H.dot(y - prev_y) + + return d, gnew, crvmin def trsbox(xopt, g, H, sl, su, delta, use_fortran=USE_FORTRAN): @@ -405,8 +485,63 @@ def ball_step(x0, g, Delta): if sqrt(gsqnorm) < ZERO_THRESH: # Error catching: if g=0, make no step return 0.0 else: - return (sqrt(gdotx0**2 + gsqnorm*(Delta**2 - x0sqnorm)) - gdotx0) / gsqnorm + # Sqrt had negative input on prob 46 in OG DFOLS with noise + # print("Inside of the sqrt:", gdotx0**2 + gsqnorm*(Delta**2 - x0sqnorm)) + # Got Inside of the sqrt: -3.608971127647144e-42 + # Added max(0,...) here + return (sqrt(np.maximum(0,gdotx0**2 + gsqnorm*(Delta**2 - x0sqnorm))) - gdotx0) / gsqnorm + +def ctrsbox_linear(xbase, g, projections, Delta, d_max_iters=100, d_tol=1e-10, use_fortran=USE_FORTRAN): + # Solve the convex program: + # min_d g' * d + # s.t. xbase + d is feasible w.r.t. constraint set C + # ||d||^2 <= Delta^2 + + n = g.size + d = np.zeros((n,)) + y = d.copy() + t = 1 + dirn = -g + cons_dirns = [] + + # If g[i] = 0, never step along this direction + constant_directions = np.where(np.abs(dirn) < ZERO_THRESH)[0] + dirn[constant_directions] = 0.0 + + # trust region is a ball of radius delta centered around xbase + trproj = lambda w: pball(w, xbase, Delta) + # combine trust region constraints with user-entered constraints + P = projections.copy() + P.append(trproj) + def proj(d0): + p = dykstra(P, xbase + d0, max_iter=d_max_iters, tol=d_tol) + # we want the step only, so we subtract + # xbase from the new point: proj(xk + d) - xk + return p - xbase + + MAX_LOOP_ITERS = 100 * n ** 2 + + # projected GD loop + for ii in range(MAX_LOOP_ITERS): + w = y + dirn + prev_d = d.copy() + d = proj(w) + + s = d - prev_d + stplen = np.linalg.norm(s) + + # exit condition + if stplen <= ZERO_THRESH: + break + + # 'momentum' update + prev_t = t + t = (1 + np.sqrt(1 + 4 * t ** 2))/2 + prev_y = y.copy() + y = d + s*(prev_t - 1)/t + + return d def trsbox_linear(g, a_in, b_in, Delta, use_fortran=USE_FORTRAN): # Solve the convex program: @@ -466,6 +601,22 @@ def trsbox_linear(g, a_in, b_in, Delta, use_fortran=USE_FORTRAN): dirn[idx_hit] = 0.0 # no more searching this direction return x +def ctrsbox_geometry(xbase, c, g, projections, Delta, d_max_iters=100, d_tol=1e-10, use_fortran=USE_FORTRAN): + # Given a Lagrange polynomial defined by: L(x) = c + g' * (x - xbase) + # Maximise |L(x)| in a box + trust region - that is, solve: + # max_x abs(c + g' * (x - xbase)) + # s.t. x is feasible w.r.t constraint set C + # ||x-xbase|| <= Delta + # Setting s = x-xbase (or x = xbase + s), this is equivalent to: + # max_s abs(c + g' * s) + # s.t. xbase + s is is feasible w.r.t constraint set C + # ||s|| <= Delta + smin = ctrsbox_linear(xbase, g, projections, Delta, d_max_iters=100, d_tol=1e-10, use_fortran=use_fortran) # minimise g' * s + smax = ctrsbox_linear(xbase, -g, projections, Delta, d_max_iters=100, d_tol=1e-10, use_fortran=use_fortran) # maximise g' * s + if abs(c + np.dot(g, smin)) >= abs(c + np.dot(g, smax)): # choose the one with largest absolute value + return smin + else: + return smax def trsbox_geometry(xbase, c, g, lower, upper, Delta, use_fortran=USE_FORTRAN): # Given a Lagrange polynomial defined by: L(x) = c + g' * (x - xbase) diff --git a/dfols/util.py b/dfols/util.py index 6107e09..154e041 100644 --- a/dfols/util.py +++ b/dfols/util.py @@ -27,11 +27,14 @@ import logging import numpy as np +import scipy.linalg as LA import sys +import pdb + __all__ = ['sumsq', 'eval_least_squares_objective', 'model_value', 'random_orthog_directions_within_bounds', - 'random_directions_within_bounds', 'apply_scaling', 'remove_scaling'] + 'random_directions_within_bounds', 'apply_scaling', 'remove_scaling', 'pbox', 'pball', 'dykstra', 'qr_rank'] def sumsq(x): @@ -207,3 +210,51 @@ def remove_scaling(x_scaled, scaling_changes): shift, scale = scaling_changes return shift + x_scaled * scale + +def dykstra(P,x0,max_iter=100,tol=1.0e-10): + x = x0.copy() + p = len(P) + y = np.zeros((p,x0.shape[0])) + + n = 0 + cI = float('inf') + while n < max_iter and cI >= tol: + cI = 0 + for i in range(0,p): + # Update iterate + prev_x = x.copy() + x = P[i](prev_x - y[i,:]) + + # Update increment + # pdb.set_trace() + prev_y = y[i,:].copy() + y[i,:] = x - (prev_x - prev_y) + + # Stop condition + cI += np.linalg.norm(prev_y - y[i,:])**2 + + n += 1 + + return x + + +def pball(x,c,r): + return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c) + + +def pbox(x,l,u): + return np.minimum(np.maximum(x,l), u) + +''' +Calculates rank of square matrix with QR. +We use the fact that the rank of a square matrix A +can be given by the number of nonzero diagonal elements of +R in the QR factorization of A. +''' +def qr_rank(A,tol=1e-25): + m,n = A.shape + assert m == n, "Input matrix must be square" + Q,R = LA.qr(A) + D = np.abs(np.diag(R)) + rank = np.sum(D > tol) + return rank, D diff --git a/dfols/version.py b/dfols/version.py index 94b452c..dc26bd5 100644 --- a/dfols/version.py +++ b/dfols/version.py @@ -22,4 +22,4 @@ """ -__version__ = '1.2.3' +__version__ = '1.3.0' From d32b9523e6fd40168707993ae317b402121527cb Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Mon, 11 Oct 2021 17:04:58 -0400 Subject: [PATCH 02/11] Change error message to be more suitable --- dfols/solver.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/dfols/solver.py b/dfols/solver.py index cb487ef..0c7ee60 100644 --- a/dfols/solver.py +++ b/dfols/solver.py @@ -871,7 +871,7 @@ def solve(objfun, x0, args=(), bounds=None, projections=[], npt=None, rhobeg=Non if projections and scaling_within_bounds: scaling_within_bounds = False - warnings.warn("Ignoring scaling_within_bounds=True for black-box constrained problem", RuntimeWarning) + warnings.warn("Ignoring scaling_within_bounds=True for problem with arbitrary constraints", RuntimeWarning) if xl is None: xl = -1e20 * np.ones((n,)) # unconstrained From 0990ef7b9c3f039ba896ae04f0c102e107394659 Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Tue, 12 Oct 2021 15:38:28 -0400 Subject: [PATCH 03/11] Add tests for TR subproblem. Make curvature calc more robust. --- dfols/tests/test_trust_region.py | 354 ++++++++++--------------------- dfols/trust_region.py | 2 +- 2 files changed, 112 insertions(+), 244 deletions(-) diff --git a/dfols/tests/test_trust_region.py b/dfols/tests/test_trust_region.py index 840d1f1..d2dd2fd 100644 --- a/dfols/tests/test_trust_region.py +++ b/dfols/tests/test_trust_region.py @@ -30,6 +30,8 @@ from dfols.trust_region import ctrsbox, ctrsbox_geometry, trsbox, trsbox_geometry from dfols.util import model_value +import pdb + def cauchy_pt(g, H, delta): # General expression for the Cauchy point @@ -73,167 +75,8 @@ def cauchy_pt_box(g, H, delta, lower, upper): def p_box(x,l,u): return np.minimum(np.maximum(x,l), u) -class TestUncInternalCDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([1.0, 0.0, 1.0]) - H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) - Delta = 2.0 - xopt = np.ones((n,)) # trying nonzero (since bounds inactive) - sl = -1e20 * np.ones((n,)) - su = 1e20 * np.ones((n,)) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([-1.0, 0.0, -0.5]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer for internal minimum? - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') - print(crvmin) - self.assertAlmostEqual(crvmin, 1.2, 'Wrong crvmin') - -class TestUncBdryCDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([1.0, 0.0, 1.0]) - H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) - Delta = 5.0 / 12.0 - xopt = np.zeros((n,)) - sl = -1e20 * np.ones((n,)) - su = 1e20 * np.ones((n,)) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') - self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') - -class TestUncBdry2CDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([1.0, 0.0, 1.0]) - H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) - Delta = 5.0 / 12.0 - xopt = np.zeros((n,)) - sl = -1e20 * np.ones((n,)) - su = 1e20 * np.ones((n,)) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.allclose(gnew, g + H.dot(d)), 'Wrong gnew') - self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') - -class TestUncBdry3CDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([0.0, 0.0, 1.0]) - H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) - Delta = 0.5 - xopt = np.zeros((n,)) - sl = -1e20 * np.ones((n,)) - su = 1e20 * np.ones((n,)) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([0.0, 0.0, -0.5]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') - self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') - # self.assertAlmostEqual(crvmin, crvmin_cauchy, 'Wrong crvmin') - -class TestUncHardCDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([0.0, 0.0, 1.0]) - H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) - Delta = sqrt(2.0) - xopt = np.zeros((n,)) - sl = -1e20 * np.ones((n,)) - su = 1e20 * np.ones((n,)) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([1.0, 0.0, -1.0]) # non-unique solution - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, H, Delta) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') - self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin') - -class TestConInternalCDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([1.0, 0.0, 1.0]) - H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) - Delta = 2.0 - xopt = np.ones((n,)) # trying nonzero (since bounds inactive) - sl = xopt + np.array([-0.5, -10.0, -10.0]) - su = xopt + np.array([10.0, 10.0, 10.0]) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([-1.0, 0.0, -0.5]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer for internal minimum? - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl-xopt, su-xopt) - # print(s_cauchy) - # print(d) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') - print(crvmin) - self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin') - - -# Notes: Gets correct min and gnew. Incorrect crvmin (1.0999999999999999). -class TestConBdryCDFO(unittest.TestCase): - def runTest(self): - n = 3 - g = np.array([1.0, 0.0, 1.0]) - H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) - Delta = 5.0 / 12.0 - xopt = np.zeros((n,)) - sl = xopt + np.array([-0.3, -0.01, -0.1]) - su = xopt + np.array([10.0, 1.0, 10.0]) - pbox = lambda x: p_box(x,sl,su) - d, gnew, crvmin = ctrsbox(xopt, g, H, sl, su, [], Delta) - true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) - est_min = model_value(g, H, d) - true_min = model_value(g, H, true_d) - # Hope to get actual correct answer - # self.assertTrue(np.all(d == true_d), 'Wrong answer') - # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') - s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl - xopt, su - xopt) - self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') - self.assertTrue(np.max(np.abs(gnew - g - H.dot(d))) < 1e-10, 'Wrong gnew') - print(crvmin) - self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin') - # self.assertAlmostEqual(crvmin, crvmin_cauchy, 'Wrong crvmin') +def p_ball(x,c,r): + return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c) class TestUncInternal(unittest.TestCase): @@ -507,108 +350,133 @@ def runTest(self): self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') -class TestGeomCDFO(unittest.TestCase): - def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([1.0, -1.0]) - a = np.array([-2.0, -2.0]) - b = np.array([1.0, 2.0]) - delta = 2.0 - c = -1.0 - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([-sqrt(2.0), sqrt(2.0)]) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') - - -class TestGeom2CDFO(unittest.TestCase): - def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([1.0, -1.0]) - a = np.array([-2.0, -2.0]) - b = np.array([1.0, 2.0]) - delta = 5.0 - c = -1.0 - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([-2.0, 2.0]) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') - - +# DFO-LS with arbitrary constraints class TestGeom3CDFO(unittest.TestCase): def runTest(self): xbase = np.array([0.0, 0.0]) + 1 g = np.array([1.0, -1.0]) a = np.array([-2.0, -2.0]) + 1 b = np.array([1.0, 2.0]) + 1 + proj = lambda x: p_box(x,a,b) delta = 5.0 c = 3.0 # may want to max instead - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([1.0, -2.0]) + 1 + x = ctrsbox_geometry(xbase, c, g, [proj], delta) + xtrue = np.array([1.0, -2.0]) self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') +class TestUncInternalCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 2.0 + xopt = np.ones((n,)) # trying nonzero (since bounds inactive) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [], Delta) + true_d = np.array([-1.0, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + s_cauchy, red_cauchy, _crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') -class TestGeomOldBugCDFO(unittest.TestCase): +class TestUncBdryCDFO(unittest.TestCase): def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([-1.0, -1.0]) - a = np.array([-2.0, -2.0]) - b = np.array([0.1, 0.9]) - delta = sqrt(2.0) - c = -1.0 # may want to max instead - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = b - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') - # self.assertFalse(True, "bad") + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [], Delta) + true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + s_cauchy, red_cauchy, _crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.allclose(gnew, g + H.dot(d)), 'Wrong gnew') -class TestGeomOldBug2CDFO(unittest.TestCase): +class TestUncHardCDFO(unittest.TestCase): def runTest(self): - xbase = np.array([0.0, 0.0, 0.0]) - g = np.array([-1.0, -1.0, -1.0]) - a = np.array([-2.0, -2.0, -2.0]) - b = np.array([0.9, 0.1, 5.0]) - delta = sqrt(3.0) - c = -1.0 # may want to max instead - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([0.9, 0.1, sqrt(3.0 - 0.81 - 0.01)]) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') - # self.assertFalse(True, "bad") + n = 3 + g = np.array([0.0, 0.0, 1.0]) + H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]]) + Delta = sqrt(2.0) + xopt = np.zeros((n,)) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [], Delta) + true_d = np.array([1.0, 0.0, -1.0]) # non-unique solution + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + s_cauchy, red_cauchy, _crvmin_cauchy = cauchy_pt(g, H, Delta) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.allclose(gnew, g + H.dot(d)), 'Wrong gnew') -class TestGeom2WithZerosCDFO(unittest.TestCase): +class TestConInternalCDFO(unittest.TestCase): def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([0.0, -1.0]) - a = np.array([-2.0, -2.0]) - b = np.array([1.0, 2.0]) - delta = 5.0 - c = 0.0 - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([0.0, 2.0]) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 2.0 + xopt = np.ones((n,)) # trying nonzero (since bounds inactive) + sl = xopt + np.array([-0.5, -10.0, -10.0]) + su = xopt + np.array([10.0, 10.0, 10.0]) + proj = lambda x: p_box(x,sl,su) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [proj], Delta) + true_d = np.array([-1.0, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + s_cauchy, red_cauchy, _crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl-xopt, su-xopt) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew') +class TestConBdryCDFO(unittest.TestCase): + def runTest(self): + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + sl = xopt + np.array([-0.3, -0.01, -0.1]) + su = xopt + np.array([10.0, 1.0, 10.0]) + proj = lambda x: p_box(x,sl,su) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [proj], Delta) + true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + s_cauchy, red_cauchy, _crvmin_cauchy = cauchy_pt_box(g, H, Delta, sl - xopt, su - xopt) + self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') + self.assertTrue(np.max(np.abs(gnew - g - H.dot(d))) < 1e-10, 'Wrong gnew') -class TestGeom2WithAlmostZerosCDFO(unittest.TestCase): +class TestBoxBallInternalCDFO(unittest.TestCase): def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([1e-15, -1.0]) - a = np.array([-2.0, -2.0]) - b = np.array([1.0, 2.0]) - delta = 5.0 - c = 0.0 - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([0.0, 2.0]) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 2.0 + xopt = np.ones((n,)) # trying nonzero (since bounds inactive) + sl = xopt + np.array([-0.5, -10.0, -10.0]) + su = xopt + np.array([10.0, 10.0, 10.0]) + boxproj = lambda x: p_box(x,sl,su) + ballproj = lambda x: p_ball(x,xopt,5) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [boxproj,ballproj], Delta) + true_d = np.array([-0.5, 0.0, -0.5]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + self.assertTrue(est_min <= true_min + 1e-3, 'Sufficient decrease not achieved') -class TestGeom2WithAlmostZeros2CDFO(unittest.TestCase): +class TestBoxBallBdryCDFO(unittest.TestCase): def runTest(self): - xbase = np.array([0.0, 0.0]) - g = np.array([1e-15, 0.0]) - a = np.array([-2.0, -2.0]) - b = np.array([1.0, 2.0]) - delta = 5.0 - c = 0.0 - x = ctrsbox_geometry(xbase, c, g, a, b, [], delta) - xtrue = np.array([0.0, 0.0]) - # print(x) - # print(xtrue) - self.assertTrue(np.max(np.abs(x - xtrue)) < 1e-10, 'Wrong step') + n = 3 + g = np.array([1.0, 0.0, 1.0]) + H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) + Delta = 5.0 / 12.0 + xopt = np.zeros((n,)) + sl = xopt + np.array([-0.3, -0.01, -0.1]) + su = xopt + np.array([10.0, 1.0, 10.0]) + boxproj = lambda x: p_box(x,sl,su) + ballproj = lambda x: p_ball(x,xopt,0.25) + d, gnew, _crvmin = ctrsbox(xopt, g, H, [boxproj,ballproj], Delta) + true_d = np.array([-0.22913085, 0.0, -0.09999527]) + est_min = model_value(g, H, d) + true_min = model_value(g, H, true_d) + self.assertTrue(est_min <= true_min + 1e-3, 'Sufficient decrease not achieved') diff --git a/dfols/trust_region.py b/dfols/trust_region.py index 8b0a21d..74ce269 100644 --- a/dfols/trust_region.py +++ b/dfols/trust_region.py @@ -133,7 +133,7 @@ def proj(d0): gnew += H.dot(s) # update CRVMIN - crv = s.dot(H).dot(s)/sumsq(s) + crv = s.dot(H).dot(s)/sumsq(s) if sumsq(s) >= ZERO_THRESH else crvmin crvmin = min(crvmin, crv) if crvmin != -1.0 else crv # exit condition From 3ba2e3f965f6c5752912abfe962f1ca32e5cb614 Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Tue, 12 Oct 2021 16:03:28 -0400 Subject: [PATCH 04/11] Add tests for solver and remove pdb in TR tests --- dfols/tests/test_solver.py | 25 +++++++++++++++++++++++++ dfols/tests/test_trust_region.py | 2 -- 2 files changed, 25 insertions(+), 2 deletions(-) diff --git a/dfols/tests/test_solver.py b/dfols/tests/test_solver.py index 9c43445..b0601ad 100644 --- a/dfols/tests/test_solver.py +++ b/dfols/tests/test_solver.py @@ -41,6 +41,13 @@ def rosenbrock_jacobian(x): return np.array([[-20.0*x[0], 10.0], [-1.0, 0.0]]) +def p_box(x,l,u): + return np.minimum(np.maximum(x,l), u) + +def p_ball(x,c,r): + return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c) + + class TestNans(unittest.TestCase): # Generic objective that only returns NaNs (like optclim code) # Verify get a sensible termination @@ -185,3 +192,21 @@ def runTest(self): self.assertTrue(array_compare(soln.jacobian, jac(soln.x), thresh=1e-1), "Wrong Jacobian") self.assertTrue(abs(soln.f) < 1e-10, "Wrong fmin") + +class TestRosenbrockBoxBall(unittest.TestCase): + # Minimise the (2d) Rosenbrock function, where x[1] hits the upper bound + def runTest(self): + # n, m = 2, 2 + x0 = np.array([-1.2, 0.7]) # standard start point does not satisfy bounds + lower = np.array([0.7, -2.0]) + upper = np.array([1.0, 2]) + boxproj = lambda x: p_box(x,lower,upper) + ballproj = lambda x: p_ball(x,np.array([0.5,1]),0.25) + xmin = np.array([0.70424386, 0.85583188]) # approximate + fmin = np.dot(rosenbrock(xmin), rosenbrock(xmin)) + soln = dfols.solve(rosenbrock, x0, projections=[boxproj,ballproj]) + print(soln.x) + self.assertTrue(array_compare(soln.x, xmin, thresh=1e-2), "Wrong xmin") + self.assertTrue(array_compare(soln.resid, rosenbrock(soln.x), thresh=1e-10), "Wrong resid") + self.assertTrue(array_compare(soln.jacobian, rosenbrock_jacobian(soln.x), thresh=1e-2), "Wrong Jacobian") + self.assertTrue(abs(soln.f - fmin) < 1e-4, "Wrong fmin") diff --git a/dfols/tests/test_trust_region.py b/dfols/tests/test_trust_region.py index d2dd2fd..b9561c6 100644 --- a/dfols/tests/test_trust_region.py +++ b/dfols/tests/test_trust_region.py @@ -30,8 +30,6 @@ from dfols.trust_region import ctrsbox, ctrsbox_geometry, trsbox, trsbox_geometry from dfols.util import model_value -import pdb - def cauchy_pt(g, H, delta): # General expression for the Cauchy point From 58104c7bf9bfeef278051f1cf70dcdc7f83658c8 Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Tue, 12 Oct 2021 17:16:25 -0400 Subject: [PATCH 05/11] Add more util tests and remove more pdb --- dfols/params.py | 2 +- dfols/tests/test_util.py | 133 ++++++++++++++++++++++++++++++++++++++- dfols/util.py | 7 +-- 3 files changed, 135 insertions(+), 7 deletions(-) diff --git a/dfols/params.py b/dfols/params.py index e168c01..6d36e2e 100644 --- a/dfols/params.py +++ b/dfols/params.py @@ -113,7 +113,7 @@ def __init__(self, n, npt, maxfun, objfun_has_noise=False): self.params["dykstra.d_tol"] = 1e-10 self.params["dykstra.max_iters"] = 100 # Matrix rank algorithm - self.params["matrix_rank.r_tol"] = 1e-16 + self.params["matrix_rank.r_tol"] = 1e-15 self.params_changed = {} for p in self.params: diff --git a/dfols/tests/test_util.py b/dfols/tests/test_util.py index f497904..57ecfab 100644 --- a/dfols/tests/test_util.py +++ b/dfols/tests/test_util.py @@ -165,4 +165,135 @@ def runTest(self): self.assertTrue(np.linalg.norm(dirns[i, :]) <= delta + 1e-10, "Unconstrained: dirn %i too long" % i) self.assertTrue(np.all(dirns[i, :] >= lower), "Direction %i below lower bound" % i) self.assertTrue(np.all(dirns[i, :] <= upper), "Direction %i above upper bound" % i) - # self.assertTrue(False, "bad") \ No newline at end of file + # self.assertTrue(False, "bad") + +# Trivial case of full rank +class TestMatrixRankQR1(unittest.TestCase): + def runTest(self): + mr_tol = 1e-15 + A = np.array([ + [1,0,0,0], + [0,1,0,0], + [0,0,1,0], + [0,0,0,1]]) + rank, D = qr_rank(A,mr_tol) + self.assertTrue(np.all(D > mr_tol), "Incorrect diagonal matrix output") + self.assertTrue(rank == 4, "Incorrect rank output") + +# Full rank but QR has negative entries for diag(R) +class TestMatrixRankQR2(unittest.TestCase): + def runTest(self): + mr_tol = 1e-15 + A = np.array([ + [1,2,3,4], + [0,6,7,8], + [-1,-2,-2,-1], + [4,2,2,1]]) + rank, D = qr_rank(A,mr_tol) + self.assertTrue(np.all(D > mr_tol), "Incorrect diagonal matrix output") + self.assertTrue(rank == 4, "Incorrect rank output") + + +# Full rank but QR has negative entries for diag(R) +class TestMatrixRankQR3(unittest.TestCase): + def runTest(self): + mr_tol = 1e-15 + A = np.array([ + [1,2,3,4], + [2,6,4,8], + [-1,-2,-3,-4], + [1,3,2,4]]) + rank, D = qr_rank(A,mr_tol) + self.assertTrue(np.all(D[0:2] > mr_tol), "Incorrect diagonal matrix output (rows 1,2)") + self.assertTrue(np.all(D[2:4] <= mr_tol), "Incorrect diagonal matrix output (rows 3,4)") + self.assertTrue(rank == 2, "Incorrect rank output") + + +class TestDykstraBoxInt(unittest.TestCase): + def runTest(self): + x0 = np.array([0,0]) + lower = np.array([-0.01, -0.1]) + upper = np.array([0.01, 0.5]) + boxproj = lambda x: pbox(x,lower,upper) + P = [boxproj] + xproj = dykstra(P,x0) + self.assertTrue(np.all(xproj == x0), "Incorrect point returned by Dykstra") + + +class TestDykstraBoxExt(unittest.TestCase): + def runTest(self): + x0 = np.array([-2,5]) + lower = np.array([-1, -1]) + upper = np.array([0.5, 0.9]) + boxproj = lambda x: pbox(x,lower,upper) + P = [boxproj] + xproj = dykstra(P,x0) + xtrue = np.array([-1,0.9]) + self.assertTrue(np.allclose(xproj, xtrue), "Incorrect point returned by Dykstra") + +class TestDykstraBallInt(unittest.TestCase): + def runTest(self): + x0 = np.array([0,0]) + ballproj = lambda x: pball(x,x0+1,2) + P = [ballproj] + xproj = dykstra(P,x0) + self.assertTrue(np.all(xproj == x0), "Incorrect point returned by Dykstra") + + +class TestDykstraBallExt(unittest.TestCase): + def runTest(self): + x0 = np.array([-3,5]) + ballproj = lambda x: pball(x,np.array([-0.5,1]),1) + P = [ballproj] + xproj = dykstra(P,x0) + xtrue = np.array([-1.02999894, 1.8479983]) + self.assertTrue(np.allclose(xproj, xtrue), "Incorrect point returned by Dykstra") + + +class TestDykstraBoxBallInt(unittest.TestCase): + def runTest(self): + x0 = np.array([0.72,1.1]) + lower = np.array([0.7, -2.0]) + upper = np.array([1.0, 2]) + boxproj = lambda x: pbox(x,lower,upper) + ballproj = lambda x: pball(x,np.array([0.5,1]),0.25) + P = [boxproj,ballproj] + xproj = dykstra(P,x0) + self.assertTrue(np.all(xproj == x0), "Incorrect point returned by Dykstra") + +class TestDykstraBoxBallExt1(unittest.TestCase): + def runTest(self): + x0 = np.array([0,4]) + lower = np.array([0.7, -2.0]) + upper = np.array([1.0, 2]) + boxproj = lambda x: pbox(x,lower,upper) + ballproj = lambda x: pball(x,np.array([0.5,1]),0.25) + P = [boxproj,ballproj] + xproj = dykstra(P,x0) + xtrue = np.array([0.6940582, 1.1576116]) + self.assertTrue(np.allclose(xproj, xtrue), "Incorrect point returned by Dykstra") + + +class TestDykstraBoxBallExt2(unittest.TestCase): + def runTest(self): + x0 = np.array([0.8,-3]) + lower = np.array([0.7, -2.0]) + upper = np.array([1.0, 2]) + boxproj = lambda x: pbox(x,lower,upper) + ballproj = lambda x: pball(x,np.array([0.5,1]),0.25) + P = [boxproj,ballproj] + xproj = dykstra(P,x0) + xtrue = np.array([0.68976232, 0.8372417]) + self.assertTrue(np.allclose(xproj, xtrue), "Incorrect point returned by Dykstra") + + +class TestDykstraBoxBallBdry(unittest.TestCase): + def runTest(self): + x0 = np.array([0.7,0.85]) + lower = np.array([0.7, -2.0]) + upper = np.array([1.0, 2]) + boxproj = lambda x: pbox(x,lower,upper) + ballproj = lambda x: pball(x,np.array([0.5,1]),0.25) + P = [boxproj,ballproj] + xproj = dykstra(P,x0) + self.assertTrue(np.allclose(xproj, x0), "Incorrect point returned by Dykstra") diff --git a/dfols/util.py b/dfols/util.py index 154e041..02c9884 100644 --- a/dfols/util.py +++ b/dfols/util.py @@ -30,8 +30,6 @@ import scipy.linalg as LA import sys -import pdb - __all__ = ['sumsq', 'eval_least_squares_objective', 'model_value', 'random_orthog_directions_within_bounds', 'random_directions_within_bounds', 'apply_scaling', 'remove_scaling', 'pbox', 'pball', 'dykstra', 'qr_rank'] @@ -211,7 +209,7 @@ def remove_scaling(x_scaled, scaling_changes): return shift + x_scaled * scale -def dykstra(P,x0,max_iter=100,tol=1.0e-10): +def dykstra(P,x0,max_iter=100,tol=1e-10): x = x0.copy() p = len(P) y = np.zeros((p,x0.shape[0])) @@ -226,7 +224,6 @@ def dykstra(P,x0,max_iter=100,tol=1.0e-10): x = P[i](prev_x - y[i,:]) # Update increment - # pdb.set_trace() prev_y = y[i,:].copy() y[i,:] = x - (prev_x - prev_y) @@ -251,7 +248,7 @@ def pbox(x,l,u): can be given by the number of nonzero diagonal elements of R in the QR factorization of A. ''' -def qr_rank(A,tol=1e-25): +def qr_rank(A,tol=1e-15): m,n = A.shape assert m == n, "Input matrix must be square" Q,R = LA.qr(A) From 4bf0d53c1cbc628d0cab485306ca025c2e7e420c Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Sat, 16 Oct 2021 21:55:14 -0400 Subject: [PATCH 06/11] Add constrained example --- examples/rosenbrock_constrained.py | 31 ++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 examples/rosenbrock_constrained.py diff --git a/examples/rosenbrock_constrained.py b/examples/rosenbrock_constrained.py new file mode 100644 index 0000000..eeac7bf --- /dev/null +++ b/examples/rosenbrock_constrained.py @@ -0,0 +1,31 @@ +# DFO-LS example: minimize the Rosenbrock function with arbitrary convex constraints +from __future__ import print_function +import numpy as np +import dfols + +# Define the objective function +def rosenbrock(x): + return np.array([10.0 * (x[1] - x[0] ** 2), 1.0 - x[0]]) + +# Define the starting point +x0 = np.array([-1.2, 1]) + +def pball(x): + c = np.array([0.7,1.5]) # ball centre + r = 0.4 # ball radius + return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c) + +def pbox(x): + l = np.array([-2, 1.1]) # lower bound + u = np.array([0.9, 3]) # upper bound + return np.minimum(np.maximum(x,l), u) + +# For optional extra output details +import logging +logging.basicConfig(level=logging.DEBUG, format='%(message)s') + +# Call DFO-LS +soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox]) + +# Display output +print(soln) From 30ee963ae6f04f1f23afdcd9336910cbef6a7084 Mon Sep 17 00:00:00 2001 From: Matt Hough Date: Sat, 16 Oct 2021 23:24:34 -0400 Subject: [PATCH 07/11] Add examples and update docs --- dfols/params.py | 2 +- dfols/tests/test_util.py | 12 +- docs/advanced.rst | 9 + docs/build/doctrees/advanced.doctree | Bin 84560 -> 87990 bytes docs/build/doctrees/diagnostic.doctree | Bin 22026 -> 22021 bytes docs/build/doctrees/environment.pickle | Bin 34653 -> 36240 bytes docs/build/doctrees/history.doctree | Bin 15063 -> 15890 bytes docs/build/doctrees/index.doctree | Bin 13924 -> 14340 bytes docs/build/doctrees/info.doctree | Bin 34483 -> 34775 bytes docs/build/doctrees/install.doctree | Bin 17426 -> 17421 bytes docs/build/doctrees/userguide.doctree | Bin 86188 -> 91374 bytes docs/build/html/.buildinfo | 2 +- docs/build/html/_sources/advanced.rst.txt | 9 + docs/build/html/_sources/history.rst.txt | 4 + docs/build/html/_sources/index.rst.txt | 6 +- docs/build/html/_sources/info.rst.txt | 5 +- docs/build/html/_sources/userguide.rst.txt | 45 +- .../html/_static/documentation_options.js | 2 +- docs/build/html/_static/pygments.css | 6 +- docs/build/html/advanced.html | 21 +- docs/build/html/diagnostic.html | 4 +- docs/build/html/genindex.html | 4 +- docs/build/html/history.html | 11 +- docs/build/html/index.html | 19 +- docs/build/html/info.html | 13 +- docs/build/html/install.html | 4 +- docs/build/html/objects.inv | Bin 401 -> 399 bytes docs/build/html/search.html | 4 +- docs/build/html/searchindex.js | 2 +- docs/build/html/userguide.html | 52 +- docs/build/latex/DFOLS.aux | 199 +-- docs/build/latex/DFOLS.fdb_latexmk | 365 ++--- docs/build/latex/DFOLS.fls | 888 ++++++++++- docs/build/latex/DFOLS.log | 1386 ++++++----------- docs/build/latex/DFOLS.out | 43 +- docs/build/latex/DFOLS.pdf | Bin 302355 -> 321015 bytes docs/build/latex/DFOLS.tex | 104 +- docs/build/latex/DFOLS.toc | 109 +- docs/build/latex/sphinxhighlight.sty | 134 +- docs/history.rst | 4 + docs/index.rst | 6 +- docs/info.rst | 5 +- docs/userguide.rst | 45 +- examples/rosenbrock_constrained.py | 3 +- manual.pdf | Bin 302355 -> 321015 bytes 45 files changed, 2029 insertions(+), 1498 deletions(-) mode change 100644 => 100755 manual.pdf diff --git a/dfols/params.py b/dfols/params.py index 6d36e2e..af7b93c 100644 --- a/dfols/params.py +++ b/dfols/params.py @@ -113,7 +113,7 @@ def __init__(self, n, npt, maxfun, objfun_has_noise=False): self.params["dykstra.d_tol"] = 1e-10 self.params["dykstra.max_iters"] = 100 # Matrix rank algorithm - self.params["matrix_rank.r_tol"] = 1e-15 + self.params["matrix_rank.r_tol"] = 1e-18 self.params_changed = {} for p in self.params: diff --git a/dfols/tests/test_util.py b/dfols/tests/test_util.py index 57ecfab..51c1b30 100644 --- a/dfols/tests/test_util.py +++ b/dfols/tests/test_util.py @@ -170,7 +170,7 @@ def runTest(self): # Trivial case of full rank class TestMatrixRankQR1(unittest.TestCase): def runTest(self): - mr_tol = 1e-15 + mr_tol = 1e-18 A = np.array([ [1,0,0,0], [0,1,0,0], @@ -183,7 +183,7 @@ def runTest(self): # Full rank but QR has negative entries for diag(R) class TestMatrixRankQR2(unittest.TestCase): def runTest(self): - mr_tol = 1e-15 + mr_tol = 1e-18 A = np.array([ [1,2,3,4], [0,6,7,8], @@ -194,15 +194,15 @@ def runTest(self): self.assertTrue(rank == 4, "Incorrect rank output") -# Full rank but QR has negative entries for diag(R) +# Not full rank class TestMatrixRankQR3(unittest.TestCase): def runTest(self): - mr_tol = 1e-15 + mr_tol = 1e-18 A = np.array([ [1,2,3,4], [2,6,4,8], - [-1,-2,-3,-4], - [1,3,2,4]]) + [0,0,0,0], + [0,0,0,0]]) rank, D = qr_rank(A,mr_tol) self.assertTrue(np.all(D[0:2] > mr_tol), "Incorrect diagonal matrix output (rows 1,2)") self.assertTrue(np.all(D[2:4] <= mr_tol), "Incorrect diagonal matrix output (rows 3,4)") diff --git a/docs/advanced.rst b/docs/advanced.rst index 6073888..1303bee 100644 --- a/docs/advanced.rst +++ b/docs/advanced.rst @@ -103,6 +103,15 @@ Dynamically Growing Initial Set * :code:`growing.gamma_dec` - Trust region decrease parameter during the growing phase. Default is :code:`tr_radius.gamma_dec`. * :code:`growing.num_new_dirns_each_iter` - Number of new search directions to add with each iteration where we do not have a full set of search directions. Default is 0, as this approach is not recommended. +Dykstra's Algorithm +------------------------------- +* :code:`dykstra.d_tol` - Tolerance on the stopping conditions of Dykstra's algorithm. Default is :math:`10^{-10}`. +* :code:`dykstra.max_iters` - The maximum number of iterations Dykstra's algorithm is allowed to take before stopping. Default is :math:`100`. + +Checking Matrix Rank +------------------------------- +* :code:`matrix_rank.r_tol` - Tolerance on what is the smallest posisble diagonal entry value in the QR factorization before being considered zero. 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zw%lHT7b%w2)R{1o?Ff{eGhw(~R|t!le-Pb#v9hTMJeZG|M7bkFc{J92Pp=?xNQ72+C%8+HABcDuU2Z73+~B{2jTu7>4}|xwi%U diff --git a/docs/build/html/.buildinfo b/docs/build/html/.buildinfo index 3bc5cd9..987e588 100644 --- a/docs/build/html/.buildinfo +++ b/docs/build/html/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. -config: 7851303ebe6ed71f013a86e86fbeadbc +config: f48a4434832128cee1c37b97e0d08ba7 tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/build/html/_sources/advanced.rst.txt b/docs/build/html/_sources/advanced.rst.txt index 6073888..1303bee 100644 --- a/docs/build/html/_sources/advanced.rst.txt +++ b/docs/build/html/_sources/advanced.rst.txt @@ -103,6 +103,15 @@ Dynamically Growing Initial Set * :code:`growing.gamma_dec` - Trust region decrease parameter during the growing phase. Default is :code:`tr_radius.gamma_dec`. * :code:`growing.num_new_dirns_each_iter` - Number of new search directions to add with each iteration where we do not have a full set of search directions. Default is 0, as this approach is not recommended. +Dykstra's Algorithm +------------------------------- +* :code:`dykstra.d_tol` - Tolerance on the stopping conditions of Dykstra's algorithm. Default is :math:`10^{-10}`. +* :code:`dykstra.max_iters` - The maximum number of iterations Dykstra's algorithm is allowed to take before stopping. Default is :math:`100`. + +Checking Matrix Rank +------------------------------- +* :code:`matrix_rank.r_tol` - Tolerance on what is the smallest posisble diagonal entry value in the QR factorization before being considered zero. Default is :math:`10^{-18}`. + References ---------- diff --git a/docs/build/html/_sources/history.rst.txt b/docs/build/html/_sources/history.rst.txt index fd4d8ef..c9c8e60 100644 --- a/docs/build/html/_sources/history.rst.txt +++ b/docs/build/html/_sources/history.rst.txt @@ -45,3 +45,7 @@ Version 1.2.2 (26 Feb 2021) Version 1.2.3 (1 Jun 2021) --------------------------- * Minor update to customise handling of NaNs in objective evaluations - no changes to the DFO-LS algorithm. + +Version 1.3.0 (16 Oct 2021) +--------------------------- +* Handle finitely many arbitrary convex constraints in addition to simple bound constraints. diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt index a0e467e..3668752 100644 --- a/docs/build/html/_sources/index.rst.txt +++ b/docs/build/html/_sources/index.rst.txt @@ -11,16 +11,16 @@ DFO-LS: Derivative-Free Optimizer for Least-Squares Minimization **Author:** `Lindon Roberts `_ -DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional bound constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares. +DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional convex constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares. That is, DFO-LS solves .. math:: \min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ - \text{s.t.} &\quad a \leq x \leq b + \text{s.t.} &\quad x \in C -The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds). +The constraint set :math:`C` is assumed to be non-empty, closed and convex. Moreover, the constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible). Full details of the DFO-LS algorithm are given in our paper: C. Cartis, J. Fiala, B. Marteau and L. Roberts, `Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers `_, *ACM Transactions on Mathematical Software*, 45:3 (2019), pp. 32:1-32:41 [`preprint `_] . DFO-LS is a more flexible version of `DFO-GN `_. diff --git a/docs/build/html/_sources/info.rst.txt b/docs/build/html/_sources/info.rst.txt index 824a232..46d74c8 100644 --- a/docs/build/html/_sources/info.rst.txt +++ b/docs/build/html/_sources/info.rst.txt @@ -3,14 +3,15 @@ Overview When to use DFO-LS ------------------ -DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional bound constraints) +DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional convex constraints). .. math:: \min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ - \text{s.t.} &\quad a \leq x \leq b + \text{s.t.} &\quad x \in C We call :math:`f(x)` the objective function and :math:`r_i(x)` the residual functions (or simply residuals). +Here :math:`C` is a non-empty and closed convex set. DFO-LS is a *derivative-free* optimization algorithm, which means it does not require the user to provide the derivatives of :math:`f(x)` or :math:`r_i(x)`, nor does it attempt to estimate them internally (by using finite differencing, for instance). diff --git a/docs/build/html/_sources/userguide.rst.txt b/docs/build/html/_sources/userguide.rst.txt index 6804892..28408bd 100644 --- a/docs/build/html/_sources/userguide.rst.txt +++ b/docs/build/html/_sources/userguide.rst.txt @@ -9,9 +9,9 @@ DFO-LS is designed to solve the local optimization problem .. math:: \min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ - \text{s.t.} &\quad a \leq x \leq b + \text{s.t.} &\quad x \in C -where the bound constraints :math:`a \leq x \leq b` are optional. The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds). +where the set :math:`C` is an optional non-empty, closed and convex constraint set. The constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible). DFO-LS iteratively constructs an interpolation-based model for the objective, and determines a step using a trust-region framework. For an in-depth technical description of the algorithm see the paper [CFMR2018]_. @@ -75,6 +75,7 @@ These arguments are: * :code:`args` - a tuple of extra arguments passed to the objective function. * :code:`bounds` - a tuple :code:`(lower, upper)` with the vectors :math:`a` and :math:`b` of lower and upper bounds on :math:`x` (default is :math:`a_i=-10^{20}` and :math:`b_i=10^{20}`). To set bounds for either :code:`lower` or :code:`upper`, but not both, pass a tuple :code:`(lower, None)` or :code:`(None, upper)`. +* :code:`projections` - a list :code:`[f1,f2,...,fn]` of functions that each take as input a point :code:`x` and return a new point :code:`y`. The new point :code:`y` should be given by the projection of :code:`x` onto a closed convex set. The intersection of all sets corresponding to a function must be non-empty. * :code:`npt` - the number of interpolation points to use (default is :code:`len(x0)+1`). If using restarts, this is the number of points to use in the first run of the solver, before any restarts (and may be optionally increased via settings in :code:`user_params`). * :code:`rhobeg` - the initial value of the trust region radius (default is :math:`0.1\max(\|x_0\|_{\infty}, 1)`, or 0.1 if :code:`scaling_within_bounds`). * :code:`rhoend` - minimum allowed value of trust region radius, which determines when a successful termination occurs (default is :math:`10^{-8}`). @@ -142,9 +143,9 @@ Note that DFO-LS is a randomized algorithm: in its first phase, it builds an int This and all following problems can be found in the `examples `_ directory on the DFO-LS Github page. -Adding Bounds and More Output +Adding Constraints and More Output ----------------------------- -We can extend the above script to add constraints. To do this, we can add the lines +We can extend the above script to add constraints. To add bound constraints alone, we can add the lines .. code-block:: python @@ -179,6 +180,40 @@ However, we also get a warning that our starting point was outside of the bounds DFO-LS automatically fixes this, and moves :math:`x_0` to a point within the bounds, in this case :math:`x_0=(-1.2,0.85)`. +If we want more complex constraints, we can instead write + + .. code-block:: python + + # Define the projection functions + def pball(x): + c = np.array([0.7,1.5]) # ball centre + r = 0.4 # ball radius + return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c) + + def pbox(x): + l = np.array([-2, 1.1]) # lower bound + u = np.array([0.9, 3]) # upper bound + return np.minimum(np.maximum(x,l), u) + + # Call DFO-LS (with box and ball constraints) + soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox]) + +DFO-LS correctly finds the solution to this constrained problem too: + + .. code-block:: none + + ****** DFO-LS Results ****** + Solution xmin = [0.9 1.15358984] + Residual vector = [3.43589838 0.1 ] + Objective value f(xmin) = 11.81539771 + Needed 10 objective evaluations (at 10 points) + Approximate Jacobian = [[-1.79826221e+01 1.00004412e+01] + [-1.00000000e+00 6.81262102e-15]] + Exit flag = 0 + Success: rho has reached rhoend + **************************** + + We can also get DFO-LS to print out more detailed information about its progress using the `logging `_ module. To do this, we need to add the following lines: .. code-block:: python @@ -188,7 +223,7 @@ We can also get DFO-LS to print out more detailed information about its progress # ... (call dfols.solve) -And we can now see each evaluation of :code:`objfun`: +And for the simple bounds example we can now see each evaluation of :code:`objfun`: .. code-block:: none diff --git a/docs/build/html/_static/documentation_options.js b/docs/build/html/_static/documentation_options.js index 5dfebe0..7cf0629 100644 --- a/docs/build/html/_static/documentation_options.js +++ b/docs/build/html/_static/documentation_options.js @@ -1,6 +1,6 @@ var DOCUMENTATION_OPTIONS = { URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), - VERSION: '1.2.3', + VERSION: '1.3.0', LANGUAGE: 'None', COLLAPSE_INDEX: false, BUILDER: 'html', diff --git a/docs/build/html/_static/pygments.css b/docs/build/html/_static/pygments.css index 691aeb8..de7af26 100644 --- a/docs/build/html/_static/pygments.css +++ b/docs/build/html/_static/pygments.css @@ -1,7 +1,7 @@ pre { line-height: 125%; } -td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } -span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } -td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +td.linenos pre { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; } +span.linenos { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; } +td.linenos pre.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } .highlight .hll { background-color: #ffffcc } .highlight { background: #eeffcc; } diff --git a/docs/build/html/advanced.html b/docs/build/html/advanced.html index 8ca5d90..ae72a6d 100644 --- a/docs/build/html/advanced.html +++ b/docs/build/html/advanced.html @@ -8,7 +8,7 @@ - Advanced Usage — DFO-LS v1.2.3 documentation + Advanced Usage — DFO-LS v1.3.0 documentation @@ -61,7 +61,7 @@
- 1.2.3 + 1.3.0
@@ -102,6 +102,8 @@
  • Regression Model Management
  • Multiple Restarts
  • Dynamically Growing Initial Set
    • +
  • Dykstra’s Algorithm
    • +
  • Checking Matrix Rank
  • References
    • @@ -174,7 +176,7 @@

    Advanced Usage¶

    This section describes different optional user parameters available in DFO-LS.

    -

    In the last section (Using DFO-LS), we introduced dfols.solve(), which has the optional input user_params. This is a Python dictionary of user parameters. We will now go through the settings which can be changed in this way. More details are available in the paper [CFMR2018].

    +

    In the last section (Using DFO-LS), we introduced dfols.solve(), which has the optional input user_params. This is a Python dictionary of user parameters. We will now go through the settings which can be changed in this way. More details are available in the paper [CFMR2018].

    The default values, used if no override is given, in some cases vary depending on whether objfun has stochastic noise; that is, whether evaluating objfun(x) several times at the same x gives the same result or not. Whether or not this is the case is determined by the objfun_has_noise input to dfols.solve() (and not by inspecting objfun, for instance).

    +
    +

    Dykstra’s Algorithm¶

    +
      +

    • dykstra.d_tol - Tolerance on the stopping conditions of Dykstra’s algorithm. Default is \(10^{-10}\).

      • +

    • dykstra.max_iters - The maximum number of iterations Dykstra’s algorithm is allowed to take before stopping. Default is \(100\).

      • +
    +
    +
    +

    Checking Matrix Rank¶

    +
      +

    • matrix_rank.r_tol - Tolerance on what is the smallest posisble diagonal entry value in the QR factorization before being considered zero. Default is \(10^{-18}\).

      • +
    +

    References¶

    diff --git a/docs/build/html/diagnostic.html b/docs/build/html/diagnostic.html index f4e5a4c..6c5e667 100644 --- a/docs/build/html/diagnostic.html +++ b/docs/build/html/diagnostic.html @@ -8,7 +8,7 @@ - Diagnostic Information — DFO-LS v1.2.3 documentation + Diagnostic Information — DFO-LS v1.3.0 documentation @@ -61,7 +61,7 @@
    - 1.2.3 + 1.3.0
    diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html index ab3ee15..96042a4 100644 --- a/docs/build/html/genindex.html +++ b/docs/build/html/genindex.html @@ -9,7 +9,7 @@ - Index — DFO-LS v1.2.3 documentation + Index — DFO-LS v1.3.0 documentation @@ -60,7 +60,7 @@
    - 1.2.3 + 1.3.0
    diff --git a/docs/build/html/history.html b/docs/build/html/history.html index 8d70630..6169770 100644 --- a/docs/build/html/history.html +++ b/docs/build/html/history.html @@ -8,7 +8,7 @@ - Version History — DFO-LS v1.2.3 documentation + Version History — DFO-LS v1.3.0 documentation @@ -60,7 +60,7 @@
    - 1.2.3 + 1.3.0
    @@ -101,6 +101,7 @@
  • Version 1.2.1 (13 Feb 2020)
  • Version 1.2.2 (26 Feb 2021)
  • Version 1.2.3 (1 Jun 2021)
    • +
  • Version 1.3.0 (16 Oct 2021)
    • @@ -232,6 +233,12 @@

    Version 1.2.3 (1 Jun 2021) +

    Version 1.3.0 (16 Oct 2021)¶

    +
      +

    • Handle finitely many arbitrary convex constraints in addition to simple bound constraints.

      • +
    +

    diff --git a/docs/build/html/index.html b/docs/build/html/index.html index 76457b0..898bf06 100644 --- a/docs/build/html/index.html +++ b/docs/build/html/index.html @@ -8,7 +8,7 @@ - DFO-LS: Derivative-Free Optimizer for Least-Squares Minimization — DFO-LS v1.2.3 documentation + DFO-LS: Derivative-Free Optimizer for Least-Squares Minimization — DFO-LS v1.3.0 documentation @@ -60,7 +60,7 @@
    - 1.2.3 + 1.3.0
    @@ -158,15 +158,15 @@

    DFO-LS: Derivative-Free Optimizer for Least-Squares Minimization¶

    -

    Release: 1.2.3

    -

    Date: 01 June 2021

    +

    Release: 1.3.0

    +

    Date: 16 October 2021

    Author: Lindon Roberts

    -

    DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional bound constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.

    +

    DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional convex constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.

    That is, DFO-LS solves

    \[\begin{split}\min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ -\text{s.t.} &\quad a \leq x \leq b\end{split}\]
    -

    The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds).

    +\text{s.t.} &\quad x \in C\end{split}\]
    +

    The constraint set \(C\) is assumed to be non-empty, closed and convex. Moreover, the constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).

    Full details of the DFO-LS algorithm are given in our paper: C. Cartis, J. Fiala, B. Marteau and L. Roberts, Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers, ACM Transactions on Mathematical Software, 45:3 (2019), pp. 32:1-32:41 [preprint] . DFO-LS is a more flexible version of DFO-GN.

    If you are interested in solving general optimization problems (without a least-squares structure), you may wish to try Py-BOBYQA, which has many of the same features as DFO-LS.

    DFO-LS is released under the GNU General Public License. Please contact NAG for alternative licensing.

    @@ -194,7 +194,7 @@

    DFO-LS: Derivative-Free Optimizer for Least-Squares MinimizationHow to use DFO-LS
  • Optional Arguments
  • A Simple Example
    • -
  • Adding Bounds and More Output
    • +
  • Adding Constraints and More Output
  • Example: Noisy Objective Evaluation
  • Example: Parameter Estimation/Data Fitting
  • Example: Solving a Nonlinear System of Equations
    • @@ -213,6 +213,8 @@

    DFO-LS: Derivative-Free Optimizer for Least-Squares MinimizationRegression Model Management
  • Multiple Restarts
  • Dynamically Growing Initial Set
    • +
  • Dykstra’s Algorithm
    • +
  • Checking Matrix Rank
  • References
    • @@ -234,6 +236,7 @@

    DFO-LS: Derivative-Free Optimizer for Least-Squares MinimizationVersion 1.2.1 (13 Feb 2020)
  • Version 1.2.2 (26 Feb 2021)
  • Version 1.2.3 (1 Jun 2021)
    • +
  • Version 1.3.0 (16 Oct 2021)
    • diff --git a/docs/build/html/info.html b/docs/build/html/info.html index f3867f0..bf211f3 100644 --- a/docs/build/html/info.html +++ b/docs/build/html/info.html @@ -8,7 +8,7 @@ - Overview — DFO-LS v1.2.3 documentation + Overview — DFO-LS v1.3.0 documentation @@ -61,7 +61,7 @@
    - 1.2.3 + 1.3.0
    @@ -168,11 +168,12 @@

    Overview¶

    When to use DFO-LS¶

    -

    DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional bound constraints)

    +

    DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional convex constraints).

    \[\begin{split}\min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ -\text{s.t.} &\quad a \leq x \leq b\end{split}\]
    -

    We call \(f(x)\) the objective function and \(r_i(x)\) the residual functions (or simply residuals).

    +\text{s.t.} &\quad x \in C\end{split}\]
    +

    We call \(f(x)\) the objective function and \(r_i(x)\) the residual functions (or simply residuals). +Here \(C\) is a non-empty and closed convex set.

    DFO-LS is a derivative-free optimization algorithm, which means it does not require the user to provide the derivatives of \(f(x)\) or \(r_i(x)\), nor does it attempt to estimate them internally (by using finite differencing, for instance).

    There are two main situations when using a derivative-free algorithm (such as DFO-LS) is preferable to a derivative-based algorithm (which is the vast majority of least-squares solvers).

    If the residuals are noisy, then calculating or even estimating their derivatives may be impossible (or at least very inaccurate). By noisy, we mean that if we evaluate \(r_i(x)\) multiple times at the same value of \(x\), we get different results. This may happen when a Monte Carlo simulation is used, for instance, or \(r_i(x)\) involves performing a physical experiment.

    @@ -217,7 +218,7 @@

    Details of the DFO-LS Algorithm\(x_k\), we compute a model which approximates the objective \(m_k(s)\approx f(x_k+s)\) (for small steps \(s\)), and maintain a value \(\Delta_k>0\) (called the trust region radius) which measures the size of \(s\) for which the approximation is good.

    At each step, we compute a trial step \(s_k\) designed to make our approximation \(m_k(s)\) small (this task is called the trust region subproblem). We evaluate the objective at this new point, and if this provided a good decrease in the objective, we take the step (\(x_{k+1}=x_k+s_k\)), otherwise we stay put (\(x_{k+1}=x_k\)). Based on this information, we choose a new value \(\Delta_{k+1}\), and repeat the process.

    In DFO-LS, we construct our approximation \(m_k(s)\) by interpolating a linear approximation for each residual \(r_i(x)\) at several points close to \(x_k\). To make sure our interpolated model is accurate, we need to regularly check that the points are well-spaced, and move them if they aren’t (i.e. improve the geometry of our interpolation points).

    -

    A complete description of the DFO-LS algorithm is given in our paper [CFMR2018].

    +

    A complete description of the DFO-LS algorithm is given in our paper [CFMR2018].

    References¶

    diff --git a/docs/build/html/install.html b/docs/build/html/install.html index d74c88f..b9a3e9a 100644 --- a/docs/build/html/install.html +++ b/docs/build/html/install.html @@ -8,7 +8,7 @@ - Installing DFO-LS — DFO-LS v1.2.3 documentation + Installing DFO-LS — DFO-LS v1.3.0 documentation @@ -61,7 +61,7 @@
    - 1.2.3 + 1.3.0
    diff --git a/docs/build/html/objects.inv b/docs/build/html/objects.inv index 0a40ac70446e2f79c64912950d2f8f543bdf4bdf..540a6f6429ef5e575695ecea53587d35cac46bb8 100644 GIT binary patch delta 292 zcmV+<0o(qO1CIlcJOeW>Fp)nzf6r^fAQZm)S3KCRj&-Ne+aQz`T2ctz-No1BfzeJ) zw(PH;iDor0*iFA*zW1S!gU~ffa9(busex}mBXz)TAYTtshv>Xx&dof7X)o#*XD2V**ZULzuJoDvXGAe delta 294 zcmV+>0oneK1CaxeJOeT=Gm$?$e@jcmFc7}yR|NDLaXrc2gtEA>OBagXV>4|B^4Lw% zYW?-5O=}Ynyd~c&Gn3(B;JOAuofmsyYRYz$FW5upm837L;?40ENZly=^tgMT4U&I= zoGiTq+x946_T1f5Mg;O!8|Sf3vo|!R7n|y+8)FssXf$a-qZaU$zp|pye|nsbq(kS8 z9n&`!D5~DUx{yd;BS^N`MV%xThmxJDJuSfE5DFQ99V`GXuO1bCgQcNDdIIh|t8P8F z;OH6k#Kp2Pw2)^vCPtS7*a6`)NSx~*O9G6G@gy7#2NM - Search — DFO-LS v1.2.3 documentation + Search — DFO-LS v1.3.0 documentation @@ -60,7 +60,7 @@
    - 1.2.3 + 1.3.0
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diff --git a/docs/build/html/userguide.html b/docs/build/html/userguide.html index 5b40502..ab38f4f 100644 --- a/docs/build/html/userguide.html +++ b/docs/build/html/userguide.html @@ -8,7 +8,7 @@ - Using DFO-LS — DFO-LS v1.2.3 documentation + Using DFO-LS — DFO-LS v1.3.0 documentation @@ -61,7 +61,7 @@
    - 1.2.3 + 1.3.0
    @@ -94,7 +94,7 @@
  • How to use DFO-LS
  • Optional Arguments
  • A Simple Example
    • -
  • Adding Bounds and More Output
    • +
  • Adding Constraints and More Output
  • Example: Noisy Objective Evaluation
  • Example: Parameter Estimation/Data Fitting
  • Example: Solving a Nonlinear System of Equations
    • @@ -176,8 +176,8 @@

    Nonlinear Least-Squares Minimization \[\begin{split}\min_{x\in\mathbb{R}^n} &\quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\ -\text{s.t.} &\quad a \leq x \leq b\end{split}\]

    -

    where the bound constraints \(a \leq x \leq b\) are optional. The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds).

    +\text{s.t.} &\quad x \in C\end{split}\] +

    where the set \(C\) is an optional non-empty, closed and convex constraint set. The constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).

    DFO-LS iteratively constructs an interpolation-based model for the objective, and determines a step using a trust-region framework. For an in-depth technical description of the algorithm see the paper [CFMR2018].

    @@ -239,6 +239,7 @@

    Optional Arguments

  • args - a tuple of extra arguments passed to the objective function.

  • bounds - a tuple (lower, upper) with the vectors \(a\) and \(b\) of lower and upper bounds on \(x\) (default is \(a_i=-10^{20}\) and \(b_i=10^{20}\)). To set bounds for either lower or upper, but not both, pass a tuple (lower, None) or (None, upper).

    • +

  • projections - a list [f1,f2,...,fn] of functions that each take as input a point x and return a new point y. The new point y should be given by the projection of x onto a closed convex set. The intersection of all sets corresponding to a function must be non-empty.

  • npt - the number of interpolation points to use (default is len(x0)+1). If using restarts, this is the number of points to use in the first run of the solver, before any restarts (and may be optionally increased via settings in user_params).

  • rhobeg - the initial value of the trust region radius (default is \(0.1\max(\|x_0\|_{\infty}, 1)\), or 0.1 if scaling_within_bounds).

  • rhoend - minimum allowed value of trust region radius, which determines when a successful termination occurs (default is \(10^{-8}\)).

    • @@ -300,9 +301,9 @@

    A Simple Exampleexamples directory on the DFO-LS Github page.

    -
    -

    Adding Bounds and More Output¶

    -

    We can extend the above script to add constraints. To do this, we can add the lines

    +
    +

    Adding Constraints and More Output¶

    +

    We can extend the above script to add constraints. To add bound constraints alone, we can add the lines

    # Define bound constraints (lower <= x <= upper)
 lower = np.array([-10.0, -10.0])
@@ -335,6 +336,39 @@ 
    Adding Bounds and More Output\(x_0\) to a point within the bounds, in this case \(x_0=(-1.2,0.85)\).
    
+
    If we want more complex constraints, we can instead write
    
+
    
+
    # Define the projection functions
+def pball(x):
+    c = np.array([0.7,1.5]) # ball centre
+    r = 0.4 # ball radius
+    return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c)
+
+def pbox(x):
+    l = np.array([-2, 1.1]) # lower bound
+    u = np.array([0.9, 3]) # upper bound
+    return np.minimum(np.maximum(x,l), u)
+
+# Call DFO-LS (with box and ball constraints)
+soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
+
    
+
    
+
    
+
    DFO-LS correctly finds the solution to this constrained problem too:
    
+
    
+
    ****** DFO-LS Results ******
+Solution xmin = [0.9        1.15358984]
+Residual vector = [3.43589838 0.1       ]
+Objective value f(xmin) = 11.81539771
+Needed 10 objective evaluations (at 10 points)
+Approximate Jacobian = [[-1.79826221e+01  1.00004412e+01]
+ [-1.00000000e+00  6.81262102e-15]]
+Exit flag = 0
+Success: rho has reached rhoend
+****************************
+
    
+
    
+
    
 
    We can also get DFO-LS to print out more detailed information about its progress using the logging module. To do this, we need to add the following lines:
    
 
    
 
    import logging
@@ -344,7 +378,7 @@ 
    Adding Bounds and More Outputobjfun:
    
+
    And for the simple bounds example we can now see each evaluation of objfun:
    
 
    
 
    Function eval 1 at point 1 has f = 39.65 at x = [-1.2   0.85]
 Initialising (coordinate directions)
diff --git a/docs/build/latex/DFOLS.aux b/docs/build/latex/DFOLS.aux
index a3dc2be..dfc33b1 100755
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+++ b/docs/build/latex/DFOLS.aux
@@ -1,5 +1,7 @@
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diff --git a/docs/build/latex/DFOLS.fdb_latexmk b/docs/build/latex/DFOLS.fdb_latexmk
index c8ca9ec..c3143db 100755
--- a/docs/build/latex/DFOLS.fdb_latexmk
+++ b/docs/build/latex/DFOLS.fdb_latexmk
@@ -1,187 +1,194 @@
 # Fdb version 3
-["makeindex DFOLS.idx"] 1533896586 "DFOLS.idx" "DFOLS.ind" "DFOLS" 1622530124
-  "DFOLS.idx" 1622530123 0 d41d8cd98f00b204e9800998ecf8427e ""
+["makeindex DFOLS.idx"] 1533896586 "DFOLS.idx" "DFOLS.ind" "DFOLS" 1634440875
+  "DFOLS.idx" 1634440874 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
   (generated)
-  "DFOLS.ilg"
   "DFOLS.ind"
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  []
 
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 Chapter 4.
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diff --git a/docs/build/latex/DFOLS.out b/docs/build/latex/DFOLS.out
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z$?~cFF^)hr&KDKgtAD<)Oqq!LKO}@&fo98e>z>Y4#IxL|dKuJoN%sx>S7{Smc>Di>33)mmDLT*&Fk7rZ?(Mt-ISXdUc41xP5JOpbJ
z5miu#wM3W+rTG<(sQFIya+YI<2tk467di|?&$(tZLrK&Y#QTcbDZj5?Dr&Kp;uCB;
zc$_^EnsaLu{3^4yXwxwiK`Kd+!V(h&5_L3<^;C?x=lHExdsk9{DklhPr?Hz&yy!ynld3+Q{bxMF@x+jQ7T~VYOButwF!eN
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m9dq>8dnsKsLV1UpTCi^iPwv5zqOh`Z@o*qfQAsFCBK`_
 
-DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional bound constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.
+DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional convex constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.
 
 That is, DFO-LS solves
 
 .. math::
 
    \min_{x\in\mathbb{R}^n}  &\quad  f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\
-   \text{s.t.} &\quad  a \leq x \leq b
+   \text{s.t.} &\quad x \in C
 
-The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds).
+The constraint set :math:`C` is assumed to be non-empty, closed and convex. Moreover, the constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).
 
 Full details of the DFO-LS algorithm are given in our paper: C. Cartis, J. Fiala, B. Marteau and L. Roberts, `Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers `_, *ACM Transactions on Mathematical Software*, 45:3 (2019), pp. 32:1-32:41 [`preprint `_] . DFO-LS is a more flexible version of `DFO-GN `_.
 
diff --git a/docs/info.rst b/docs/info.rst
index 824a232..46d74c8 100644
--- a/docs/info.rst
+++ b/docs/info.rst
@@ -3,14 +3,15 @@ Overview
 
 When to use DFO-LS
 ------------------
-DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional bound constraints)
+DFO-LS is designed to solve the nonlinear least-squares minimization problem (with optional convex constraints).
 
 .. math::
 
    \min_{x\in\mathbb{R}^n}  &\quad  f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\
-   \text{s.t.} &\quad  a \leq x \leq b
+   \text{s.t.} &\quad x \in C
 
 We call :math:`f(x)` the objective function and :math:`r_i(x)` the residual functions (or simply residuals).
+Here :math:`C` is a non-empty and closed convex set.
 
 DFO-LS is a *derivative-free* optimization algorithm, which means it does not require the user to provide the derivatives of :math:`f(x)` or :math:`r_i(x)`, nor does it attempt to estimate them internally (by using finite differencing, for instance). 
 
diff --git a/docs/userguide.rst b/docs/userguide.rst
index 6804892..28408bd 100644
--- a/docs/userguide.rst
+++ b/docs/userguide.rst
@@ -9,9 +9,9 @@ DFO-LS is designed to solve the local optimization problem
 .. math::
 
    \min_{x\in\mathbb{R}^n}  &\quad  f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\
-   \text{s.t.} &\quad  a \leq x \leq b
+   \text{s.t.} &\quad x \in C
 
-where the bound constraints :math:`a \leq x \leq b` are optional. The upper and lower bounds on the variables are non-relaxable (i.e. DFO-LS will never ask to evaluate a point outside the bounds).
+where the set :math:`C` is an optional non-empty, closed and convex constraint set. The constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).
 
 DFO-LS iteratively constructs an interpolation-based model for the objective, and determines a step using a trust-region framework.
 For an in-depth technical description of the algorithm see the paper [CFMR2018]_.
@@ -75,6 +75,7 @@ These arguments are:
 
 * :code:`args` - a tuple of extra arguments passed to the objective function. 
 * :code:`bounds` - a tuple :code:`(lower, upper)` with the vectors :math:`a` and :math:`b` of lower and upper bounds on :math:`x` (default is :math:`a_i=-10^{20}` and :math:`b_i=10^{20}`). To set bounds for either :code:`lower` or :code:`upper`, but not both, pass a tuple :code:`(lower, None)` or :code:`(None, upper)`.
+* :code:`projections` - a list :code:`[f1,f2,...,fn]` of functions that each take as input a point :code:`x` and return a new point :code:`y`. The new point :code:`y` should be given by the projection of :code:`x` onto a closed convex set. The intersection of all sets corresponding to a function must be non-empty.
 * :code:`npt` - the number of interpolation points to use (default is :code:`len(x0)+1`). If using restarts, this is the number of points to use in the first run of the solver, before any restarts (and may be optionally increased via settings in :code:`user_params`).
 * :code:`rhobeg` - the initial value of the trust region radius (default is :math:`0.1\max(\|x_0\|_{\infty}, 1)`, or 0.1 if :code:`scaling_within_bounds`).
 * :code:`rhoend` - minimum allowed value of trust region radius, which determines when a successful termination occurs (default is :math:`10^{-8}`).
@@ -142,9 +143,9 @@ Note that DFO-LS is a randomized algorithm: in its first phase, it builds an int
 
 This and all following problems can be found in the `examples `_ directory on the DFO-LS Github page.
 
-Adding Bounds and More Output
+Adding Constraints and More Output
 -----------------------------
-We can extend the above script to add constraints. To do this, we can add the lines
+We can extend the above script to add constraints. To add bound constraints alone, we can add the lines
 
   .. code-block:: python
   
@@ -179,6 +180,40 @@ However, we also get a warning that our starting point was outside of the bounds
 
 DFO-LS automatically fixes this, and moves :math:`x_0` to a point within the bounds, in this case :math:`x_0=(-1.2,0.85)`.
 
+If we want more complex constraints, we can instead write
+
+  .. code-block:: python
+  
+      # Define the projection functions
+      def pball(x):
+          c = np.array([0.7,1.5]) # ball centre
+          r = 0.4 # ball radius
+          return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c)
+
+      def pbox(x):
+          l = np.array([-2, 1.1]) # lower bound
+          u = np.array([0.9, 3]) # upper bound
+          return np.minimum(np.maximum(x,l), u)
+
+      # Call DFO-LS (with box and ball constraints)
+      soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
+
+DFO-LS correctly finds the solution to this constrained problem too:
+
+  .. code-block:: none
+  
+      ****** DFO-LS Results ******
+      Solution xmin = [0.9        1.15358984]
+      Residual vector = [3.43589838 0.1       ]
+      Objective value f(xmin) = 11.81539771
+      Needed 10 objective evaluations (at 10 points)
+      Approximate Jacobian = [[-1.79826221e+01  1.00004412e+01]
+       [-1.00000000e+00  6.81262102e-15]]
+      Exit flag = 0
+      Success: rho has reached rhoend
+      ****************************
+
+
 We can also get DFO-LS to print out more detailed information about its progress using the `logging `_ module. To do this, we need to add the following lines:
 
   .. code-block:: python
@@ -188,7 +223,7 @@ We can also get DFO-LS to print out more detailed information about its progress
       
       # ... (call dfols.solve)
 
-And we can now see each evaluation of :code:`objfun`:
+And for the simple bounds example we can now see each evaluation of :code:`objfun`:
 
   .. code-block:: none
   
diff --git a/examples/rosenbrock_constrained.py b/examples/rosenbrock_constrained.py
index eeac7bf..8a0812c 100644
--- a/examples/rosenbrock_constrained.py
+++ b/examples/rosenbrock_constrained.py
@@ -10,6 +10,7 @@ def rosenbrock(x):
 # Define the starting point
 x0 = np.array([-1.2, 1])
 
+# Define the projection functions
 def pball(x):
     c = np.array([0.7,1.5]) # ball centre
     r = 0.4 # ball radius
@@ -25,7 +26,7 @@ def pbox(x):
 logging.basicConfig(level=logging.DEBUG, format='%(message)s')
 
 # Call DFO-LS
-soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
+soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox], user_params={'dykstra.d_tol': 1e-50})
 
 # Display output
 print(soln)
diff --git a/manual.pdf b/manual.pdf
old mode 100644
new mode 100755
index 3eb1243cf46aea69b21f2da3551362ab979ce540..886cb3c4b8a94283f6164b95ebe668618d27eda5
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m9dq>8dnsKsLV1UpTCi^iPwv5zqOh`Z@o*qfQAsFCBK
Date: Sun, 17 Oct 2021 18:35:52 -0400
Subject: [PATCH 08/11] Correct code that was outdated from paper

---
 dfols/controller.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/dfols/controller.py b/dfols/controller.py
index 5ace32c..a408267 100644
--- a/dfols/controller.py
+++ b/dfols/controller.py
@@ -144,7 +144,7 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa
             while k < self.n():
                 ek = np.zeros(self.n())
                 ek[k] = 1
-                p = np.dot(ek,self.delta)
+                p = np.dot(ek,min(1,self.delta))
                 yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol"))
                 D[k,:] = yk - self.model.xbase
 
@@ -158,7 +158,7 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa
                 if diag[k] < mr_tol:
                     ek = np.zeros(self.n())
                     ek[k] = 1
-                    p = -np.dot(ek,self.delta)
+                    p = -np.dot(ek,min(1,self.delta))
                     yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol"))
                     dk = D[k,:].copy()
                     D[k,:] = yk - self.model.xbase
@@ -178,7 +178,7 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa
                 if slctr[k%self.n()] == 1: # if selector says make -ve, make -ve
                     ek = np.zeros(self.n())
                     ek[k%self.n()] = 1
-                    p = -np.dot(ek,self.delta)
+                    p = -np.dot(ek,min(1,self.delta))
                     yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol"))
                     dk = D[k%self.n(),:].copy()
                     D[k%self.n(),:] = yk - self.model.xbase
@@ -202,7 +202,7 @@ def initialise_coordinate_directions(self, number_of_samples, num_directions, pa
                     if diag[k] < mr_tol:
                         p = np.random.normal(size=self.n())
                         p = p/np.linalg.norm(p)
-                        p = np.dot(p,self.delta)
+                        p = np.dot(p,min(1,self.delta))
                         yk = dykstra(self.model.projections, self.model.xbase + p, max_iter=params("dykstra.max_iters"), tol=params("dykstra.d_tol"))
                         dk = D[k,:].copy()
                         D[k,:] = yk - self.model.xbase

From 6c7e1528e63ccc573b2ec28e9c82435c440f8bf9 Mon Sep 17 00:00:00 2001
From: Matt Hough 
Date: Mon, 18 Oct 2021 00:24:54 -0400
Subject: [PATCH 09/11] Remove unwanted params in example

---
 examples/rosenbrock_constrained.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/rosenbrock_constrained.py b/examples/rosenbrock_constrained.py
index 8a0812c..e69c0e7 100644
--- a/examples/rosenbrock_constrained.py
+++ b/examples/rosenbrock_constrained.py
@@ -26,7 +26,7 @@ def pbox(x):
 logging.basicConfig(level=logging.DEBUG, format='%(message)s')
 
 # Call DFO-LS
-soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox], user_params={'dykstra.d_tol': 1e-50})
+soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
 
 # Display output
 print(soln)

From 3b2309d7e9cbfecd66dca52cbf4a0326465d9a3c Mon Sep 17 00:00:00 2001
From: Matt Hough 
Date: Mon, 25 Oct 2021 12:20:36 -0400
Subject: [PATCH 10/11] Add warning when using projections and get model
 increase in tr subproblem

---
 dfols/controller.py                        |  10 ++++++--
 docs/build/doctrees/environment.pickle     | Bin 36240 -> 36246 bytes
 docs/build/doctrees/userguide.doctree      | Bin 91374 -> 92677 bytes
 docs/build/html/_sources/userguide.rst.txt |  20 ++++++++-------
 docs/build/html/objects.inv                | Bin 399 -> 401 bytes
 docs/build/html/searchindex.js             |   2 +-
 docs/build/html/userguide.html             |  18 +++++++------
 docs/build/latex/DFOLS.aux                 |   6 ++---
 docs/build/latex/DFOLS.fdb_latexmk         |  24 +++++++++---------
 docs/build/latex/DFOLS.log                 |  26 ++++++++-----------
 docs/build/latex/DFOLS.pdf                 | Bin 321015 -> 321478 bytes
 docs/build/latex/DFOLS.tex                 |  28 ++++++++++++---------
 docs/userguide.rst                         |  20 ++++++++-------
 manual.pdf                                 | Bin 321015 -> 321478 bytes
 14 files changed, 83 insertions(+), 71 deletions(-)

diff --git a/dfols/controller.py b/dfols/controller.py
index a408267..32e3e37 100644
--- a/dfols/controller.py
+++ b/dfols/controller.py
@@ -43,6 +43,7 @@
            'EXIT_INPUT_ERROR', 'EXIT_TR_INCREASE_ERROR', 'EXIT_LINALG_ERROR', 'EXIT_FALSE_SUCCESS_WARNING',
            'EXIT_AUTO_DETECT_RESTART_WARNING']
 
+EXIT_TR_INCREASE_WARNING = 5  # warning, TR increase in proj constrained case - likely due to multiple active constraints
 EXIT_AUTO_DETECT_RESTART_WARNING = 4  # warning, auto-detected restart criteria
 EXIT_FALSE_SUCCESS_WARNING = 3  # warning, maximum fake successful steps reached
 EXIT_SLOW_WARNING = 2  # warning, maximum number of slow (successful) iterations reached
@@ -70,6 +71,8 @@ def message(self, with_stem=True):
             return "Warning (slow progress): " + self.msg
         elif self.flag == EXIT_MAXFUN_WARNING:
             return "Warning (max evals): " + self.msg
+        elif self.flag == EXIT_TR_INCREASE_WARNING:
+            return "Warning (trust region increase): " + self.msg
         elif self.flag == EXIT_INPUT_ERROR:
             return "Error (bad input): " + self.msg
         elif self.flag == EXIT_TR_INCREASE_ERROR:
@@ -82,7 +85,7 @@ def message(self, with_stem=True):
             return "Unknown exit flag: " + self.msg
 
     def able_to_do_restart(self):
-        if self.flag in [EXIT_TR_INCREASE_ERROR, EXIT_LINALG_ERROR, EXIT_SLOW_WARNING, EXIT_AUTO_DETECT_RESTART_WARNING]:
+        if self.flag in [EXIT_TR_INCREASE_ERROR, EXIT_TR_INCREASE_WARNING, EXIT_LINALG_ERROR, EXIT_SLOW_WARNING, EXIT_AUTO_DETECT_RESTART_WARNING]:
             return True
         elif self.flag in [EXIT_MAXFUN_WARNING, EXIT_INPUT_ERROR]:
             return False
@@ -616,7 +619,10 @@ def calculate_ratio(self, current_iter, rvec_list, d, gopt, H):
         if min(sqrt(sumsq(d)), self.delta) > self.rho:  # if ||d|| >= rho, successful!
             self.last_successful_iter = current_iter
         if pred_reduction < 0.0:
-            exit_info = ExitInformation(EXIT_TR_INCREASE_ERROR, "Trust region step gave model increase")
+            if len(self.model.projections) > 1: # if we are using multiple projections, only warn since likely due to constraint intersection
+                exit_info = ExitInformation(EXIT_TR_INCREASE_WARNING, "Either multiple constraints are active or trust region step gave model increase")
+            else:
+                exit_info = ExitInformation(EXIT_TR_INCREASE_ERROR, "Either rust region step gave model increase")
 
         ratio = actual_reduction / pred_reduction
         return ratio, exit_info
diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
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GIT binary patch
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diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js
index 9520167..149bcb0 100644
--- a/docs/build/html/searchindex.js
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diff --git a/docs/build/html/userguide.html b/docs/build/html/userguide.html
index ab38f4f..218f9d3 100644
--- a/docs/build/html/userguide.html
+++ b/docs/build/html/userguide.html
@@ -211,6 +211,7 @@ 
    How to use DFO-LSsoln.EXIT_MAXFUN_WARNING - maximum allowed objective evaluations reached. This is the most likely return value when using multiple restarts.
    
 
  • soln.EXIT_SLOW_WARNING - maximum number of slow iterations reached.
    • 
 
  • soln.EXIT_FALSE_SUCCESS_WARNING - DFO-LS reached the maximum number of restarts which decreased the objective, but to a worse value than was found in a previous run.
    • 
+
  • soln.EXIT_TR_INCREASE_WARNING - model increase when solving the trust region subproblem with multiple arbitrary constraints.
    • 
 
  • soln.EXIT_INPUT_ERROR - error in the inputs.
    • 
 
  • soln.EXIT_TR_INCREASE_ERROR - error occurred when solving the trust region subproblem.
    • 
 
  • soln.EXIT_LINALG_ERROR - linear algebra error, e.g. the interpolation points produced a singular linear system.
    • 
@@ -336,7 +337,7 @@ 
    Adding Constraints and More Output\(x_0\) to a point within the bounds, in this case \(x_0=(-1.2,0.85)\).
    
-
    If we want more complex constraints, we can instead write
    
+
    If we want more complex constraints, we can instead write something like the following:
    
 
    
 
    # Define the projection functions
 def pball(x):
@@ -354,17 +355,18 @@ 
    Adding Constraints and More Output
    ****** DFO-LS Results ******
-Solution xmin = [0.9        1.15358984]
-Residual vector = [3.43589838 0.1       ]
-Objective value f(xmin) = 11.81539771
+Solution xmin = [0.9        1.15359245]
+Residual vector = [3.43592448 0.1       ]
+Objective value f(xmin) = 11.81557703
 Needed 10 objective evaluations (at 10 points)
 Approximate Jacobian = [[-1.79826221e+01  1.00004412e+01]
- [-1.00000000e+00  6.81262102e-15]]
-Exit flag = 0
-Success: rho has reached rhoend
+ [-1.00000000e+00 -1.81976605e-15]]
+Exit flag = 5
+Warning (trust region increase): Either multiple constraints are active or trust region step gave model increase
 ****************************
 
    
 
    
diff --git a/docs/build/latex/DFOLS.aux b/docs/build/latex/DFOLS.aux
index dfc33b1..ae3caac 100755
--- a/docs/build/latex/DFOLS.aux
+++ b/docs/build/latex/DFOLS.aux
@@ -46,12 +46,12 @@
 \newlabel{info:parameter-fitting}{{2.2}{5}{Parameter Fitting}{section.2.2}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {2.3}Solving Nonlinear Systems of Equations}{6}{section.2.3}\protected@file@percent }
 \newlabel{info:solving-nonlinear-systems-of-equations}{{2.3}{6}{Solving Nonlinear Systems of Equations}{section.2.3}{}}
-\citation{info:cfmr2018}
+\citation{userguide:cfmr2018}
 \@writefile{toc}{\contentsline {section}{\numberline {2.4}Details of the DFO\sphinxhyphen {}LS Algorithm}{7}{section.2.4}\protected@file@percent }
 \newlabel{info:details-of-the-dfo-ls-algorithm}{{2.4}{7}{Details of the DFO\sphinxhyphen {}LS Algorithm}{section.2.4}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {2.5}References}{7}{section.2.5}\protected@file@percent }
 \newlabel{info:references}{{2.5}{7}{References}{section.2.5}{}}
-\citation{info:cfmr2018}
+\citation{userguide:cfmr2018}
 \@writefile{toc}{\contentsline {chapter}{\numberline {3}Using DFO\sphinxhyphen {}LS}{9}{chapter.3}\protected@file@percent }
 \@writefile{lof}{\addvspace {10\p@ }}
 \@writefile{lot}{\addvspace {10\p@ }}
@@ -75,7 +75,7 @@
 \newlabel{userguide:example-solving-a-nonlinear-system-of-equations}{{3.8}{18}{Example: Solving a Nonlinear System of Equations}{section.3.8}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {3.9}References}{19}{section.3.9}\protected@file@percent }
 \newlabel{userguide:references}{{3.9}{19}{References}{section.3.9}{}}
-\citation{info:cfmr2018}
+\citation{userguide:cfmr2018}
 \@writefile{toc}{\contentsline {chapter}{\numberline {4}Advanced Usage}{21}{chapter.4}\protected@file@percent }
 \@writefile{lof}{\addvspace {10\p@ }}
 \@writefile{lot}{\addvspace {10\p@ }}
diff --git a/docs/build/latex/DFOLS.fdb_latexmk b/docs/build/latex/DFOLS.fdb_latexmk
index c3143db..ffe90bb 100755
--- a/docs/build/latex/DFOLS.fdb_latexmk
+++ b/docs/build/latex/DFOLS.fdb_latexmk
@@ -1,10 +1,10 @@
 # Fdb version 3
-["makeindex DFOLS.idx"] 1533896586 "DFOLS.idx" "DFOLS.ind" "DFOLS" 1634440875
-  "DFOLS.idx" 1634440874 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
+["makeindex DFOLS.idx"] 1533896586 "DFOLS.idx" "DFOLS.ind" "DFOLS" 1635178686
+  "DFOLS.idx" 1635178685 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
   (generated)
-  "DFOLS.ind"
   "DFOLS.ilg"
-["pdflatex"] 1634440872 "DFOLS.tex" "DFOLS.pdf" "DFOLS" 1634440875
+  "DFOLS.ind"
+["pdflatex"] 1635178684 "DFOLS.tex" "DFOLS.pdf" "DFOLS" 1635178686
   "/etc/texmf/web2c/texmf.cnf" 1624242784 475 c0e671620eb5563b2130f56340a5fde8 ""
   "/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab ""
   "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
@@ -173,22 +173,22 @@
   "/usr/share/texmf/web2c/texmf.cnf" 1613593815 38841 799d1dd9682a55ce442e10c99777ecc1 ""
   "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1624243066 5160710 ecf427ae8fa19139d8691f526e47bb9b ""
   "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1624243094 2569235 be2903e90bfe54d2770ce0f508f15937 ""
-  "DFOLS.aux" 1634440874 14077 a57e9cbc321455cf71aa897afa283d2c "pdflatex"
+  "DFOLS.aux" 1635178686 14092 9d9d9e97af3301fe1a6671e122c87eb2 "pdflatex"
   "DFOLS.ind" 1610358580 0 d41d8cd98f00b204e9800998ecf8427e "makeindex DFOLS.idx"
-  "DFOLS.out" 1634440874 9566 4c15cb7f3428ba1015be450cf20ae095 "pdflatex"
-  "DFOLS.tex" 1634440863 88436 83d524cb5461f8777e2e649ff2ddefdb ""
-  "DFOLS.toc" 1634440874 4715 c361968e0fbff7dd069132047d694ae5 "pdflatex"
+  "DFOLS.out" 1635178686 9566 4c15cb7f3428ba1015be450cf20ae095 "pdflatex"
+  "DFOLS.tex" 1635178681 88954 c0e52f684f29b5b7b470a229b4c94cfb ""
+  "DFOLS.toc" 1635178686 4715 c361968e0fbff7dd069132047d694ae5 "pdflatex"
   "data_fitting.png" 1610358580 29893 211bb1c28ea25d47c8c0990fbf39c55c ""
   "footnotehyper-sphinx.sty" 1610358580 8888 1bbd7bdeae8c8bed1d10d551bddb1cc9 ""
   "sphinx.sty" 1633985769 82020 a38700b8aa22dfd94a8a5b905e69be73 ""
-  "sphinxhighlight.sty" 1634440869 8137 38a433148fcb7611515a989ff1750dd5 ""
+  "sphinxhighlight.sty" 1635178681 8137 38a433148fcb7611515a989ff1750dd5 ""
   "sphinxmanual.cls" 1610358580 4236 124cd90deb92742b5d3922bfc2cd70c0 ""
-  "sphinxmessages.sty" 1634440869 745 3f5fcd6cdd7964ed608767954a8ced6f ""
+  "sphinxmessages.sty" 1635178681 745 3f5fcd6cdd7964ed608767954a8ced6f ""
   "sphinxmulticell.sty" 1610358580 14606 0b6edc2b1a83546ed92026d1f6a311b5 ""
   (generated)
-  "DFOLS.aux"
-  "DFOLS.log"
   "DFOLS.idx"
+  "DFOLS.aux"
   "DFOLS.toc"
   "DFOLS.pdf"
+  "DFOLS.log"
   "DFOLS.out"
diff --git a/docs/build/latex/DFOLS.log b/docs/build/latex/DFOLS.log
index 153396a..f0c4f81 100755
--- a/docs/build/latex/DFOLS.log
+++ b/docs/build/latex/DFOLS.log
@@ -1,4 +1,4 @@
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+This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.6.21)  25 OCT 2021 12:18
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 [15] [16]
 
 File: data_fitting.png Graphic file (type png)
 
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+Package pdftex.def Info: data_fitting.png  used on input line 861.
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 Chapter 4.
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+Underfull \hbox (badness 10000) in paragraph at lines 1089--1090
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-Underfull \hbox (badness 10000) in paragraph at lines 1120--1121
+Underfull \hbox (badness 10000) in paragraph at lines 1124--1125
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+Underfull \hbox (badness 8000) in paragraph at lines 1159--1160
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+Output written on DFOLS.pdf (37 pages, 321478 bytes).
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Date: Sun, 7 Nov 2021 01:02:43 -0500
Subject: [PATCH 11/11] Update docs and examples

---
 docs/build/doctrees/environment.pickle     | Bin 36246 -> 36753 bytes
 docs/build/doctrees/history.doctree        | Bin 15890 -> 16631 bytes
 docs/build/doctrees/index.doctree          | Bin 14340 -> 14644 bytes
 docs/build/doctrees/info.doctree           | Bin 34775 -> 35617 bytes
 docs/build/doctrees/userguide.doctree      | Bin 92677 -> 98907 bytes
 docs/build/html/_sources/history.rst.txt   |   1 +
 docs/build/html/_sources/index.rst.txt     |   7 +-
 docs/build/html/_sources/info.rst.txt      |   5 +-
 docs/build/html/_sources/userguide.rst.txt | 126 +++-
 docs/build/html/_static/pygments.css       |   6 +-
 docs/build/html/advanced.html              |  67 +-
 docs/build/html/diagnostic.html            |  29 +-
 docs/build/html/genindex.html              |   2 +-
 docs/build/html/history.html               |  50 +-
 docs/build/html/index.html                 |  27 +-
 docs/build/html/info.html                  |  34 +-
 docs/build/html/install.html               |  29 +-
 docs/build/html/search.html                |   2 +-
 docs/build/html/searchindex.js             |   2 +-
 docs/build/html/userguide.html             | 171 +++--
 docs/build/latex/DFOLS.aux                 |  23 +-
 docs/build/latex/DFOLS.fdb_latexmk         |  77 +-
 docs/build/latex/DFOLS.fls                 | 792 +--------------------
 docs/build/latex/DFOLS.log                 | 450 ++++++------
 docs/build/latex/DFOLS.out                 |  79 +-
 docs/build/latex/DFOLS.pdf                 | Bin 321478 -> 324914 bytes
 docs/build/latex/DFOLS.tex                 | 155 ++--
 docs/build/latex/DFOLS.toc                 |  11 +-
 docs/build/latex/sphinxhighlight.sty       | 134 ++--
 docs/history.rst                           |   1 +
 docs/index.rst                             |   7 +-
 docs/info.rst                              |   5 +-
 docs/userguide.rst                         | 126 +++-
 examples/rosenbrock_constrained.py         |  34 +-
 manual.pdf                                 | Bin 321478 -> 324914 bytes
 35 files changed, 989 insertions(+), 1463 deletions(-)

diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
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diff --git a/docs/build/doctrees/history.doctree b/docs/build/doctrees/history.doctree
index c8a9010aa79add5e4ab2cec1f902bb2bf2faf423..665337cb53d17f065e5e9dee919c22e40ab51b70 100755
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diff --git a/docs/build/doctrees/index.doctree b/docs/build/doctrees/index.doctree
index a87d31bf8267aeadba8b94582694ef8ff316add2..9fc32b2b36a02daecdb4c68a02f23d809eb3d07a 100755
GIT binary patch
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diff --git a/docs/build/doctrees/info.doctree b/docs/build/doctrees/info.doctree
index 1302d15f3a1035ebf2397664b61b643aac070245..a431aac09a2f4c25a2c6312ce4dbce4966562b04 100755
GIT binary patch
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zCircN;CGx}I(612a)q$F(K1teH`_
 
-DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional convex constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.
+DFO-LS is a flexible package for finding local solutions to nonlinear least-squares minimization problems (with optional constraints), without requiring any derivatives of the objective. DFO-LS stands for Derivative-Free Optimizer for Least-Squares.
 
 That is, DFO-LS solves
 
 .. math::
 
    \min_{x\in\mathbb{R}^n}  &\quad  f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\
-   \text{s.t.} &\quad x \in C
+   \text{s.t.} &\quad x \in C\\
+               &\quad  a \leq x \leq b
 
-The constraint set :math:`C` is assumed to be non-empty, closed and convex. Moreover, the constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).
+The constraint set :math:`C` is the intersection of multiple convex sets provided as input by the user. All constraints are non-relaxable (i.e. DFO-LS will never ask to evaluate a point that is not feasible).
 
 Full details of the DFO-LS algorithm are given in our paper: C. Cartis, J. Fiala, B. Marteau and L. Roberts, `Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers `_, *ACM Transactions on Mathematical Software*, 45:3 (2019), pp. 32:1-32:41 [`preprint `_] . DFO-LS is a more flexible version of `DFO-GN `_.
 
diff --git a/docs/build/html/_sources/info.rst.txt b/docs/build/html/_sources/info.rst.txt
index 46d74c8..e4e0b29 100644
--- a/docs/build/html/_sources/info.rst.txt
+++ b/docs/build/html/_sources/info.rst.txt
@@ -8,10 +8,11 @@ DFO-LS is designed to solve the nonlinear least-squares minimization problem (wi
 .. math::
 
    \min_{x\in\mathbb{R}^n}  &\quad  f(x) := \sum_{i=1}^{m}r_{i}(x)^2 \\
-   \text{s.t.} &\quad x \in C
+   \text{s.t.} &\quad x \in C\\
+               &\quad  a \leq x \leq b
 
 We call :math:`f(x)` the objective function and :math:`r_i(x)` the residual functions (or simply residuals).
-Here :math:`C` is a non-empty and closed convex set.
+:math:`C` is the intersection of multiple convex sets given as input by the user.
 
 DFO-LS is a *derivative-free* optimization algorithm, which means it does not require the user to provide the derivatives of :math:`f(x)` or :math:`r_i(x)`, nor does it attempt to estimate them internally (by using finite differencing, for instance). 
 
diff --git a/docs/build/html/_sources/userguide.rst.txt b/docs/build/html/_sources/userguide.rst.txt
index f7c5fe3..e8a7b54 100644
--- a/docs/build/html/_sources/userguide.rst.txt
+++ b/docs/build/html/_sources/userguide.rst.txt
@@ -144,7 +144,7 @@ Note that DFO-LS is a randomized algorithm: in its first phase, it builds an int
 
 This and all following problems can be found in the `examples `_ directory on the DFO-LS Github page.
 
-Adding Constraints and More Output
+Adding Bounds and More Output
 -----------------------------
 We can extend the above script to add constraints. To add bound constraints alone, we can add the lines
 
@@ -181,41 +181,6 @@ However, we also get a warning that our starting point was outside of the bounds
 
 DFO-LS automatically fixes this, and moves :math:`x_0` to a point within the bounds, in this case :math:`x_0=(-1.2,0.85)`.
 
-If we want more complex constraints, we can instead write something like the following:
-
-  .. code-block:: python
-  
-      # Define the projection functions
-      def pball(x):
-          c = np.array([0.7,1.5]) # ball centre
-          r = 0.4 # ball radius
-          return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c)
-
-      def pbox(x):
-          l = np.array([-2, 1.1]) # lower bound
-          u = np.array([0.9, 3]) # upper bound
-          return np.minimum(np.maximum(x,l), u)
-
-      # Call DFO-LS (with box and ball constraints)
-      soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
-
-DFO-LS correctly finds the solution to this constrained problem too. Note that we get a warning because the step computed in the trust region subproblem
-gave an increase in the model. This is common in the case where multiple constraints are active at the optimal point.
-
-  .. code-block:: none
-
-      ****** DFO-LS Results ******
-      Solution xmin = [0.9        1.15359245]
-      Residual vector = [3.43592448 0.1       ]
-      Objective value f(xmin) = 11.81557703
-      Needed 10 objective evaluations (at 10 points)
-      Approximate Jacobian = [[-1.79826221e+01  1.00004412e+01]
-       [-1.00000000e+00 -1.81976605e-15]]
-      Exit flag = 5
-      Warning (trust region increase): Either multiple constraints are active or trust region step gave model increase
-      ****************************
-
-
 We can also get DFO-LS to print out more detailed information about its progress using the `logging `_ module. To do this, we need to add the following lines:
 
   .. code-block:: python
@@ -259,6 +224,95 @@ An alternative option available is to get DFO-LS to print to terminal progress i
         1    55    1.00e-02  2.00e-01  1.50e-08  1.00e-08   56   
         1    56    1.00e-02  2.00e-01  1.50e-08  1.00e-08   57
 
+Handling Arbitrary Convex Constraints
+-----------------------------
+DFO-LS can also handle more general constraints where they can be written as the intersection of finitely many convex sets. For example, the below code
+minimizes the Rosenbrock function subject to a constraint set given by the intersection of two convex sets. Note the intersection of the user-provided convex
+sets must be non-empty.
+
+  .. code-block:: python
+  
+      '''
+      DFO-LS example: minimize the Rosenbrock function with arbitrary convex constraints
+
+      This example defines two functions pball(x) and pbox(x) that project onto ball and
+      box constraint sets respectively. It then passes both these functions to the DFO-LS
+      solver so that it can find a constrained minimizer to the Rosenbrock function.
+      Such a minimizer must lie in the intersection of constraint sets corresponding to
+      projection functions pball(x) and pbox(x). The description of the problem is as follows:
+
+          min rosenbrock(x)
+          s.t.
+              -2 <= x[0] <= 1.1,
+              1.1 <= x[1] <= 3,
+              norm(x-c) <= 0.4
+
+      where c = [0.7, 1.5] is the centre of the ball.
+      '''
+      from __future__ import print_function
+      import numpy as np
+      import dfols
+
+      # Define the objective function
+      def rosenbrock(x):
+          return np.array([10.0 * (x[1] - x[0] ** 2), 1.0 - x[0]])
+
+      # Define the starting point
+      x0 = np.array([-1.2, 1])
+
+      '''
+      Define ball projection function
+      Projects the input x onto a ball with
+      centre point (0.7,1.5) and radius 0.4.
+      '''
+      def pball(x):
+          c = np.array([0.7,1.5]) # ball centre
+          r = 0.4 # ball radius
+          return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c)
+
+      '''
+      Define box projection function
+      Projects the input x onto a box
+      such that -2 <= x[0] <= 0.9 and
+      1.1 <= x[1] <= 3.
+
+      Note: One could equivalently add bound
+      constraints as a separate input to the solver
+      instead.
+      '''
+      def pbox(x):
+          l = np.array([-2, 1.1]) # lower bound
+          u = np.array([0.9, 3]) # upper bound
+          return np.minimum(np.maximum(x,l), u)
+
+      # For optional extra output details
+      import logging
+      logging.basicConfig(level=logging.DEBUG, format='%(message)s')
+
+      # Call DFO-LS
+      soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
+
+      # Display output
+      print(soln)
+
+Note that for bound constraints one can choose to either implement them by defining a projection function as above, or by passing the bounds as input like in the example from the section on adding bound constraints.
+
+DFO-LS correctly finds the solution to this constrained problem too. Note that we get a warning because the step computed in the trust region subproblem
+gave an increase in the model. This is common in the case where multiple constraints are active at the optimal point.
+
+  .. code-block:: none
+
+      ****** DFO-LS Results ******
+      Solution xmin = [0.9        1.15359245]
+      Residual vector = [3.43592448 0.1       ]
+      Objective value f(xmin) = 11.81557703
+      Needed 10 objective evaluations (at 10 points)
+      Approximate Jacobian = [[-1.79826221e+01  1.00004412e+01]
+       [-1.00000000e+00 -1.81976605e-15]]
+      Exit flag = 5
+      Warning (trust region increase): Either multiple constraints are active or trust region step gave model increase
+      ****************************
+
 Example: Noisy Objective Evaluation
 -----------------------------------
 As described in :doc:`info`, derivative-free algorithms such as DFO-LS are particularly useful when :code:`objfun` has noise. Let's modify the previous example to include random noise in our objective evaluation, and compare it to a derivative-based solver:
diff --git a/docs/build/html/_static/pygments.css b/docs/build/html/_static/pygments.css
index de7af26..691aeb8 100644
--- a/docs/build/html/_static/pygments.css
+++ b/docs/build/html/_static/pygments.css
@@ -1,7 +1,7 @@
 pre { line-height: 125%; }
-td.linenos pre { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; }
-span.linenos { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; }
-td.linenos pre.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
 span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
 .highlight .hll { background-color: #ffffcc }
 .highlight { background: #eeffcc; }
diff --git a/docs/build/html/advanced.html b/docs/build/html/advanced.html
index ae72a6d..df6805c 100644
--- a/docs/build/html/advanced.html
+++ b/docs/build/html/advanced.html
@@ -5,7 +5,8 @@
   
 
   
-  
+  
+
   
   
   Advanced Usage — DFO-LS v1.3.0 documentation
@@ -85,7 +86,7 @@
               
             
             
-              
    Contents:
    
+              
    Contents:
    
 
    
 
    Depending on exactly how DFO-LS terminates, the last row of results may not be fully populated.
    
-
    
+
    
 
    Current Iterate¶
    
 
      
 
    • xk - Best point found so far (current iterate). This is only saved if user_params['logging.save_xk'] = True.
      • 
 
    • rk - The vector of residuals at the current iterate. This is only saved if user_params['logging.save_rk'] = True.
      • 
 
    • fk - The value of \(f\) at the current iterate.
      • 
 
    
-
    
-
    
+
+
    
 
    Trust Region¶
    
 
      
 
    • rho - The lower bound on the trust region radius \(\rho_k\).
      • 
 
    • delta - The trust region radius \(\Delta_k\).
      • 
 
    • norm_sk - The norm of the trust region step \(\|s_k\|\).
      • 
 
    
-
    
-
    
+
+
    
 
    Model Interpolation¶
    
 
-
    
-
    
+
+
    
 
    Iteration Count¶
    
 
-
    
-
    
+
+
    
 
    Algorithm Progress¶
    
 
      
 
    • iter_type - A text description of what type of iteration we had (e.g. Successful, Safety, etc.)
      • 
 
    • ratio - The ratio of actual to predicted objective reduction in the trust region step.
      • 
 
    • slow_iter - Equal to 1 if the current iteration is successful but slow, 0 if is successful but not slow, and -1 if was not successful.
      • 
 
    
-
    
-
    
+
+
 
 
            
    
diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
index 96042a4..3f9829a 100644
--- a/docs/build/html/genindex.html
+++ b/docs/build/html/genindex.html
@@ -84,7 +84,7 @@
               
             
             
-              
    Contents:
    
+              
    Contents: