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| Original file line number | Diff line number | Diff line change |
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| # # Sampling basis | ||
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| #md # [](@__BINDER_ROOT_URL__/generated/Getting started/sampling.ipynb) | ||
| #md # [](@__NBVIEWER_ROOT_URL__/generated/Getting started/sampling.ipynb) | ||
| # **Contributed by**: Benoît Legat | ||
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| using Test #src | ||
| using DynamicPolynomials | ||
| using SumOfSquares | ||
| import MultivariateBases as MB | ||
| import SDPLR | ||
| import Hypatia | ||
| import SCS | ||
| import BMSOS | ||
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| # In this tutorial, we show how to use a different polynomial basis | ||
| # for enforcing the equality between the polynomial and its Sum-of-Squares decomposition. | ||
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| @polyvar x | ||
| p = x^4 - 4x^3 - 2x^2 + 12x + 3 | ||
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| scs = SCS.Optimizer | ||
| sdplr = optimizer_with_attributes(SDPLR.Optimizer, "maxrank" => (m, n) -> 4) | ||
| hypatia = Hypatia.Optimizer | ||
| bmsos = BMSOS.Optimizer | ||
| function test(solver, feas::Bool) | ||
| model = Model(solver) | ||
| set_silent(model) | ||
| if feas | ||
| γ = -6 | ||
| else | ||
| @variable(model, γ) | ||
| @objective(model, Max, γ) | ||
| end | ||
| @constraint(model, p - γ in SOSCone(), zero_basis = BoxSampling([-1], [1])) | ||
| optimize!(model) | ||
| @test primal_status == MOI.FEASIBLE_POINT | ||
| if !feasible | ||
| @test value(γ) ≈ -6 rtol=1e-4 | ||
| end | ||
| end | ||
| test(scs) | ||
| test(sdplr) | ||
| test(hypatia) | ||
| test(bmsos, true) | ||
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| function test_rand(solver, d, B) | ||
| model = Model(solver) | ||
| set_silent(model) | ||
| p = MB.algebra_element(rand(2d+1), MB.SubBasis{B}(monomials(x, 0:2d))) | ||
| @constraint(model, p in SOSCone(), zero_basis = BoxSampling([-1], [1])) | ||
| optimize!(model) | ||
| return solve_time(model) | ||
| end | ||
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| test_rand(scs, 2, MultivariateBases.Trigonometric) | ||
| test_rand(bmsos, 4, MultivariateBases.Trigonometric) |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,79 @@ | ||
| struct LowRankBridge{T,M} <: MOI.Bridges.Variable.AbstractBridge | ||
| affine::Vector{MOI.ScalarAffineFunction{T}} | ||
| variables::Vector{Vector{MOI.VariableIndex}} | ||
| constraints::Vector{MOI.ConstraintIndex{MOI.VectorOfVariables}} | ||
| set::SOS.WeightedSOSCone{M} | ||
| end | ||
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| import LinearAlgebra | ||
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| function MOI.Bridges.Variable.bridge_constrained_variable( | ||
| ::Type{LowRankBridge{T,M}}, | ||
| model::MOI.ModelLike, | ||
| set::SOS.WeightedSOSCone{M}, | ||
| ) where {T,M} | ||
| variables = Vector{Vector{MOI.VariableIndex}}(undef, length(set.gram_bases)) | ||
| constraints = Vector{MOI.ConstraintIndex{MOI.VectorOfVariables}}(undef, length(set.gram_bases)) | ||
| for i in eachindex(set.gram_bases) | ||
| U = MB.transformation_to(set.gram_bases[i], set.basis) | ||
| weights = SA.coeffs(set.weights[i], set.basis) | ||
| variables[i], constraints[i] = MOI.add_constrained_variables( | ||
| model, | ||
| MOI.SetWithDotProducts( | ||
| SOS.matrix_cone(M, length(set.gram_bases[i])), | ||
| [ | ||
| MOI.TriangleVectorization( | ||
| MOI.LowRankMatrix( | ||
| [weights[j]], | ||
| reshape(U[j, :], size(U, 2), 1), | ||
| ) | ||
| ) | ||
| for j in eachindex(set.basis) | ||
| ], | ||
| ), | ||
| ) | ||
| end | ||
| return KernelBridge{T,M}( | ||
| [ | ||
| MOI.ScalarAffineFunction( | ||
| [MOI.ScalarAffineTerm(one(T), variables[i][j]) for i in eachindex(set.gram_bases)], | ||
| zero(T), | ||
| ) | ||
| for j in eachindex(set.basis) | ||
| ], | ||
| variables, | ||
| constraints, | ||
| set, | ||
| ) | ||
| end | ||
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| function MOI.Bridges.Variable.supports_constrained_variable( | ||
| ::Type{<:LowRankBridge}, | ||
| ::Type{<:SOS.WeightedSOSCone{M,B}}, | ||
| ) where {M,B} | ||
| # Could be made to work for non-LagrangeBasis but it's not low rank in | ||
| # we we'll need a high bridge cost for them so that it's only UnsafeAddMul | ||
| # if the other bridges are removed | ||
| return B <: MB.LagrangeBasis | ||
| end | ||
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| function MOI.Bridges.added_constrained_variable_types( | ||
| ::Type{LowRankBridge{T,M}}, | ||
| ) where {T,M} | ||
| return Tuple{Type}[ | ||
| (MOI.SetWithDotProducts{S[1],MOI.TriangleVectorization{MOI.LowRankMatrix{T}}},) | ||
| for S in SOS.Bridges.Constraint.constrained_variable_types(M) | ||
| if S[1] == MOI.PositiveSemidefiniteConeTriangle # FIXME hack | ||
| ] | ||
| end | ||
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| function MOI.Bridges.added_constraint_types(::Type{<:LowRankBridge}) | ||
| return Tuple{Type,Type}[] | ||
| end | ||
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| function MOI.Bridges.Variable.concrete_bridge_type( | ||
| ::Type{<:LowRankBridge{T}}, | ||
| ::Type{<:SOS.WeightedSOSCone{M}}, | ||
| ) where {T,M} | ||
| return LowRankBridge{T,M} | ||
| end |
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