/
simplex.jl
203 lines (187 loc) · 8.22 KB
/
simplex.jl
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import JuMP
function simplextest(lib::Polyhedra.Library)
hsim = HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0) ∩ HyperPlane([1, 1], 1)
vsim = convexhull([0, 1], [1, 0])
poly1 = polyhedron(hsim, lib)
@test !isempty(poly1)
center, radius = chebyshevcenter(poly1)
@test center ≈ [1/2, 1/2]
@test radius ≈ 1/2
@test dim(poly1) == 1 # FIXME doing dim earlier makes chebyshevcenter fail
inequality_fulltest(poly1, hsim)
generator_fulltest(poly1, vsim)
# Test incidence
hpidx = first(eachindex(hyperplanes(poly1)))
for ps in (incidentpoints(poly1, hpidx), get.(poly1, incidentpointindices(poly1, hpidx)))
@test (ps == [[0, 1], [1, 0]] || ps == [[1, 0], [0, 1]])
end
for hsidx in eachindex(halfspaces(poly1))
h = get(poly1, hsidx)
if dot(h.a, [1, 0]) ≈ h.β
expps = [[1, 0]]
else
@assert dot(h.a, [0, 1]) ≈ h.β
expps = [[0, 1]]
end
for ps in (incidentpoints(poly1, hsidx), get.(poly1, incidentpointindices(poly1, hsidx)))
@test ps == expps
end
end
for pidx in eachindex(points(poly1))
for hps in (incidenthyperplanes(poly1, pidx), get.(poly1, incidenthyperplaneindices(poly1, pidx)))
@test hps == [HyperPlane([1, 1], 1)]
end
for hss in (incidenthalfspaces(poly1, pidx), get.(poly1, incidenthalfspaceindices(poly1, pidx)))
h = hss[1]
@test dot(h.a, get(poly1, pidx)) ≈ h.β
end
end
@testset "Optimize with objective : max 2x_1" begin
model, T = Polyhedra.layered_optimizer(Polyhedra.linear_objective_solver(poly1))
x = MOI.add_variables(model, fulldim(poly1))
MOI.add_constraint(model, MOI.VectorOfVariables(x),
Polyhedra.PolyhedraOptSet(poly1))
MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
@test MOI.MAX_SENSE == MOI.get(model, MOI.ObjectiveSense())
MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(),
MOI.ScalarAffineFunction(
[MOI.ScalarAffineTerm{T}(2, x[1])], zero(T)))
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
@test MOI.get(model, MOI.ObjectiveValue()) == 2
@test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
@test MOI.get(model, MOI.VariablePrimal(), x[1]) == 1
@test MOI.get(model, MOI.VariablePrimal(), x[2]) == 0
end
@testset "Optimize with objective : max x_1 + 3x_2" begin
model, T = Polyhedra.layered_optimizer(Polyhedra.linear_objective_solver(poly1))
x = MOI.add_variables(model, fulldim(poly1))
MOI.add_constraint(model, MOI.VectorOfVariables(x),
Polyhedra.PolyhedraOptSet(poly1))
MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
@test MOI.MAX_SENSE == MOI.get(model, MOI.ObjectiveSense())
MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(),
MOI.ScalarAffineFunction(
[MOI.ScalarAffineTerm{T}(1, x[1]),
MOI.ScalarAffineTerm{T}(3, x[2])], zero(T)))
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
@test MOI.get(model, MOI.ObjectiveValue()) == 3
@test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
@test MOI.get(model, MOI.VariablePrimal(), x[1]) == 0
@test MOI.get(model, MOI.VariablePrimal(), x[2]) == 1
end
poly2 = polyhedron(vsim, lib)
@test dim(poly2) == 1
@test !isempty(poly2)
inequality_fulltest(poly2, hsim)
generator_fulltest(poly2, vsim)
@testset "x_1 cannot be 2" begin
hempty = hsim ∩ HyperPlane([1, 0], 2)
poly = polyhedron(hempty, lib)
@test isempty(poly)
end
# We now add the vertex (0, 0)
ext0 = convexhull([0, 0])
@test collect(points(translate(ext0, [1, 0]))) == [[1, 0]]
htri = HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0) ∩ HalfSpace([1, 1], 1)
vtri = convexhull(vsim, ext0)
convexhull!(poly1, ext0)
@test 2volume(poly1) ≈ 1
@test 2volume_simplex(poly1) ≈ 1
@test unscaled_volume_simplex(poly1) ≈ 1
inequality_fulltest(poly1, htri)
generator_fulltest(poly1, vtri)
convexhull!(poly2, ext0)
@test 2volume(poly2) ≈ 1
@test 2volume_simplex(poly1) ≈ 1
@test unscaled_volume_simplex(poly1) ≈ 1
inequality_fulltest(poly2, htri)
generator_fulltest(poly2, vtri)
# nonnegative orthant cut by x_1 + x_2 = 1
vray = conichull([1, 0], [0, 1])
poly3 = polyhedron(vray, lib)
@test_throws ErrorException chebyshevcenter(poly3)
@test dim(poly3) == 2
@testset "Optimize with objective : min x_1 + x_2" begin
model, T = Polyhedra.layered_optimizer(Polyhedra.linear_objective_solver(poly3))
x = MOI.add_variables(model, fulldim(poly3))
MOI.add_constraint(model, MOI.VectorOfVariables(x),
Polyhedra.PolyhedraOptSet(poly3))
MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
@test MOI.MIN_SENSE == MOI.get(model, MOI.ObjectiveSense())
MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(),
MOI.ScalarAffineFunction(
[MOI.ScalarAffineTerm{T}(1, x[1]),
MOI.ScalarAffineTerm{T}(1, x[2])], zero(T)))
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
@test MOI.get(model, MOI.ObjectiveValue()) == 0
@test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
@test MOI.get(model, MOI.VariablePrimal(), x[1]) == 0
@test MOI.get(model, MOI.VariablePrimal(), x[2]) == 0
end
@testset "Optimize with objective : max x_2" begin
model, T = Polyhedra.layered_optimizer(Polyhedra.linear_objective_solver(poly3))
x = MOI.add_variables(model, fulldim(poly3))
MOI.add_constraint(model, MOI.VectorOfVariables(x),
Polyhedra.PolyhedraOptSet(poly3))
MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
@test MOI.MAX_SENSE == MOI.get(model, MOI.ObjectiveSense())
MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(),
MOI.ScalarAffineFunction(
[MOI.ScalarAffineTerm{T}(1, x[2])], zero(T)))
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.DUAL_INFEASIBLE
@test MOI.get(model, MOI.ObjectiveValue()) == 1
@test MOI.get(model, MOI.PrimalStatus()) == MOI.INFEASIBILITY_CERTIFICATE
@test MOI.get(model, MOI.VariablePrimal(), x[1]) == 0
@test MOI.get(model, MOI.VariablePrimal(), x[2]) == 1
end
hcutel = HyperPlane([1, 1], 1)
hcut = intersect(hcutel)
vcut = convexhull([1, 0]) + conichull(Line([1, -1]))
@test !ininterior([1/2, 1/2], hcut)
@test inrelativeinterior([1/2, 1/2], hcut)
poly4 = copy(poly3)
polycut3 = poly3 ∩ hcutel
@test dim(polycut3) == 1
inequality_fulltest(polycut3, hsim)
generator_fulltest(polycut3, vsim)
intersect!(poly3, hcutel)
@test dim(poly3) == 1
inequality_fulltest(poly3, hsim)
generator_fulltest(poly3, vsim)
# It should not have been cut as it is a copy of poly3
@test dim(poly4) == 2
polycut4 = poly4 ∩ hcut
@test dim(polycut4) == 1
inequality_fulltest(polycut4, hsim)
generator_fulltest(polycut4, vsim)
intersect!(poly4, hcut)
@test dim(poly4) == 1
inequality_fulltest(poly4, hsim)
generator_fulltest(poly4, vsim)
# FIXME needs float currently but should be updated
# poly4 = project(poly1, [1; 0])
# inequality_fulltest(poly4, [-1; 1], [0, 1], BitSet())
# generator_fulltest(poly4, [0; 1], [])
#\
# \
# |\
# |_\
# \
hlin = HalfSpace([1, 1], 1) ∩ HalfSpace([-1, -1], -1)
plin = polyhedron(hlin, lib)
@test dim(plin) == 1
inequality_fulltest(plin, hcut)
generator_fulltest(plin, vcut)
#ineout = hrep(plin)
#@test linset(ineout) == BitSet(1)
vlin = convexhull([1, 0]) + conichull([1, -1], [-1, 1])
plin = polyhedron(vlin, lib)
inequality_fulltest(plin, hcut)
generator_fulltest(plin, vcut)
#extout = vrep(plin)
#@test linset(extout) == BitSet(1)
end