Merge pull request #160 from JuliaOpt/bl/fixed_certificate

Add support for given polynomial basis

Author: blegat

src/Certificate/Certificate.jl

@@ -127,6 +127,17 @@ function get(::Type{MaxDegree{CT, BT}}, ::GramBasisType) where {CT, BT}
     return BT
 end
 
+struct FixedBasis{CT <: SumOfSquares.SOSLikeCone, BT <: MB.AbstractPolynomialBasis} <: SimpleIdealCertificate{CT, BT}
+    cone::CT
+    basis::BT
+end
+function get(certificate::FixedBasis, ::GramBasis, poly) where CT
+    return certificate.basis
+end
+function get(::Type{FixedBasis{CT, BT}}, ::GramBasisType) where {CT, BT}
+    return BT
+end
+
 struct Newton{CT <: SumOfSquares.SOSLikeCone, BT <: MB.AbstractPolynomialBasis, NPT <: Tuple} <: SimpleIdealCertificate{CT, BT}
     cone::CT
     basis::Type{BT}

src/constraint.jl

@@ -98,7 +98,11 @@ function default_ideal_certificate(
         error("Monomial sparsity not implemented yet")
     else
         @assert sparsity isa NoSparsity
-        c = default_ideal_certificate(domain, cone, basis, newton_polytope, maxdegree)
+        if basis isa AbstractPolynomialBasis
+            c = Certificate.FixedBasis(cone, basis)
+        else
+            c = default_ideal_certificate(domain, cone, basis, newton_polytope, maxdegree)
+        end
     end
     if newton_of_remainder && !(c isa SumOfSquares.Certificate.Remainder)
         return SumOfSquares.Certificate.Remainder(c)

test/Mock/mock_tests.jl

@@ -9,6 +9,9 @@ end
 @testset "Term fixed" begin
     include("term_fixed.jl")
 end
+@testset "Quartic constant" begin
+    include("quartic_constant.jl")
+end
 @testset "Quadratic" begin
     include("quadratic.jl")
 end

test/Mock/quartic_constant.jl

@@ -0,0 +1,7 @@
+config = MOI.Test.TestConfig()
+_optimize!(mock) = MOIU.mock_optimize!(mock, [4.0, 1.0])
+for mock in mocks(_optimize!)
+    Tests.dsos_quartic_constant_test(mock, config)
+    Tests.sdsos_quartic_constant_test(mock, config)
+    Tests.sos_quartic_constant_test(mock, config)
+end

test/Tests/Tests.jl

@@ -8,6 +8,7 @@ const sd_tests = Dict{String, Function}()
 
 include("term.jl")
 include("term_fixed.jl")
+include("quartic_constant.jl")
 include("quadratic.jl")
 include("quartic_ideal.jl")
 include("univariate_sum.jl")

test/Tests/quartic_constant.jl

@@ -0,0 +1,51 @@
+using Test
+using SumOfSquares
+using DynamicPolynomials
+
+function quartic_constant_test(optimizer,
+                   config::MOIT.TestConfig,
+                   cone::SumOfSquares.PolyJuMP.PolynomialSet)
+    atol = config.atol
+    rtol = config.rtol
+
+    @polyvar x
+    p = x^4 + 4
+
+    model = _model(optimizer)
+    @variable(model, γ)
+
+    cref = @constraint(model, p - γ in cone, basis=FixedPolynomialBasis([x^2]))
+
+    @objective(model, Max, γ)
+
+    optimize!(model)
+
+    @test termination_status(model) == MOI.OPTIMAL
+
+    @test primal_status(model) == MOI.FEASIBLE_POINT
+
+    @test objective_value(model) ≈ 4 atol=atol rtol=rtol
+
+    p = gram_matrix(cref)
+    @test p isa SumOfSquares.GramMatrix
+    @test getmat(p) ≈ ones(1, 1) atol=atol rtol=rtol
+    @test p.basis isa FixedPolynomialBasis
+    @test p.basis.polynomials == [x^2]
+
+    S = SumOfSquares.SOSPolynomialSet{
+        SumOfSquares.FullSpace, Monomial{true}, MonomialVector{true},
+        SumOfSquares.Certificate.FixedBasis{typeof(cone),typeof(p.basis)}
+    }
+    @test list_of_constraint_types(model) == [(Vector{AffExpr}, S)]
+    test_delete_bridge(
+        model, cref, 1,
+        ((MOI.VectorOfVariables, MOI.Nonnegatives, 0),
+         (MOI.VectorOfVariables, MOI.PositiveSemidefiniteConeTriangle, 0)
+        ))
+end
+sos_quartic_constant_test(optimizer, config)   = quartic_constant_test(optimizer, config, SOSCone())
+sd_tests["sos_quartic_constant"] = sos_quartic_constant_test
+sdsos_quartic_constant_test(optimizer, config) = quartic_constant_test(optimizer, config, SDSOSCone())
+soc_tests["sdsos_quartic_constant"] = sdsos_quartic_constant_test
+dsos_quartic_constant_test(optimizer, config)  = quartic_constant_test(optimizer, config, DSOSCone())
+linear_tests["dsos_quartic_constant"] = dsos_quartic_constant_test