This package is the implementation of a one-phase interior point method that finds KKT points of optimization problems of the form:
where the functions 
and 
are twice differentiable. The one-phase algorithm also handles bound constraints and nonlinear equalities.
Currently, the package is in development. Although you are welcome to try it out. Please let me know if there are any bugs etc. Note that the code is generally significantly slower than Ipopt in terms of raw runtime, particularly on small problems (the iteration count is competitive). However, we recommend trying our one-phase IPM if: Ipopt is failing to solve, the problem is very large or might be infeasible.
Open the package manager (type "]" in the console) then write
add https://github.com/ohinder/advanced_timer.jl
add https://github.com/ohinder/OnePhase.git
add NLPModels@0.18.1
add JuMP@0.22.3
add NLPModelsJuMP@0.9.1
add MathOptInterface@0.10.7
test OnePhaseHere is a simple example where a JuMP model is passed to the one-phase solver
using OnePhase, JuMP
m = Model()
set_optimizer(m, OnePhase.OnePhaseSolver)
@variable(m, x, start=-3)
@NLobjective(m, Min, x)
@NLconstraint(m, x^2 >= 1.0)
@NLconstraint(m, x >= -1.0)
status = optimize!(m)Install CUTEst then run
using OnePhase, CUTEst
nlp = CUTEstModel("CHAIN")
iter, status, hist, t, err, timer = one_phase_solve(nlp);
@show get_original_x(iter) # gives the primal solution of the solver
@show get_y(iter) # gives the dual solution of the solverIf you have found some bug or think there is someway I can improve the code feel free to contact me! My webpage is https://www.oliverhinder.com/.
it = iteration number
step = step type, either stabilization step (s) or aggressive step (a)
eta = targeted reduction in feasibility/barrier parameter, eta=1 for stabilization steps eta<1 for aggressive steps
α_P = primal step size
α_D = dual step size
ls = number of points trialled during line search
|dx| = infinity norm of primal direction size
|dy| = infinity norm of dual direction size
N err = relative error in linear system solves.
mu = value of barrier parameter
dual = gradient of lagragian scaled by largest dual variable
primal = error in primal feasibility
cmp scaled = | Sy |/(1 + |y|)
inf = how close to infeasible problem is, values close to zero indicate infeasibility
delta = size of perturbation
#fac = number of factorizations (split into two numbers -- first is how many factorization needed to ensure primal schur complement is positive definite, second number represents total number of factorizations including any increases in delta to avoid issues when direction quality is very poor)
|x| = infinity norm of x variables
|y| = infinity norm of y variables
∇phi = gradient of log barrier
phi = value of log barrier
