Fix sos constraint with FixedVariablesSet

Author: blegat

src/sos_polynomial_bridge.jl

@@ -22,8 +22,12 @@ function SOSPolynomialBridge{T, F, DT, VBS, MCT, BT, MT, MVT}(
     }
     @assert MOI.output_dimension(f) == length(s.monomials)
     p = MP.polynomial(collect(MOIU.eachscalar(f)), s.monomials)
+    # As `*(::MOI.ScalarAffineFunction{T}, ::S)` is only defined if `S == T`, we
+    # need to call `changecoefficienttype`. This is critical since `T` is
+    # `Float64` when used with JuMP and the coefficient type is often `Int` if
+    # `set.domain.V` is `FullSpace` or `FixedPolynomialsSet`.
     # FIXME convert needed because the coefficient type of `r` is `Any` otherwise if `domain` is `AlgebraicSet`
-    r = convert(typeof(p), rem(p, ideal(s.domain)))
+    r = convert(typeof(p), rem(p, ideal(MP.changecoefficienttype(s.domain, T))))
     X = monomials_half_newton_polytope(MP.monomials(r), s.newton_polytope)
     Q, variable_bridge = add_matrix_variable_bridge(model, MCT, length(X), T)
     g = build_gram_matrix(Q, X)

test/Mock/mock_tests.jl

@@ -6,6 +6,9 @@ using Test, JuMP
 @testset "Term" begin
     include("term.jl")
 end
+@testset "Term fixed" begin
+    include("term_fixed.jl")
+end
 @testset "Bivariate quadratic" begin
     include("bivariate_quadratic.jl")
 end

test/Mock/term_fixed.jl

@@ -0,0 +1,8 @@
+config = MOI.Test.TestConfig()
+optimize!(mock) = MOIU.mock_optimize!(mock, [1.0, 0.0],
+    (MOI.VectorAffineFunction{Float64}, MOI.Nonnegatives) => [[1.0]],
+    (MOI.VectorAffineFunction{Float64}, MOI.Zeros) => [[1.0]])
+mock = bridged_mock(optimize!)
+Tests.sos_term_fixed_test(mock, config)
+Tests.sdsos_term_fixed_test(mock, config)
+Tests.dsos_term_fixed_test(mock, config)

test/Tests/Tests.jl

@@ -7,6 +7,7 @@ const soc_tests = Dict{String, Function}()
 const sd_tests = Dict{String, Function}()
 
 include("term.jl")
+include("term_fixed.jl")
 include("bivariate_quadratic.jl")
 include("horn.jl")
 include("concave_then_convex_cubic.jl")

test/Tests/term_fixed.jl

@@ -0,0 +1,64 @@
+using Test
+using SumOfSquares
+using DynamicPolynomials
+
+# Like `term_test` but with a variable `y` fixed to 1.
+function term_fixed_test(
+    optimizer, config::MOIT.TestConfig, cone::SumOfSquares.PolyJuMP.PolynomialSet)
+    atol = config.atol
+    rtol = config.rtol
+
+    model = _model(optimizer)
+
+    @variable(model, α)
+
+    @polyvar x y
+    set = @set y == 1
+    cref = @constraint(model, (α - 1) * x^2 * y in cone, domain = set)
+
+    @objective(model, Min, α)
+    optimize!(model)
+
+    @test termination_status(model) == MOI.OPTIMAL
+    @test objective_value(model) ≈ 1.0 atol=atol rtol=rtol
+
+    @test primal_status(model) == MOI.FEASIBLE_POINT
+    @test value(α) ≈ 1.0 atol=atol rtol=rtol
+
+    @test_throws SumOfSquares.ValueNotSupported value(cref)
+    p = gram_matrix(cref)
+    @test getmat(p) ≈ zeros(1, 1) atol=atol rtol=rtol
+    @test p.x == [x]
+
+    @test dual_status(model) == MOI.FEASIBLE_POINT
+    for (m, μ) in [(x^2 * y, dual(cref)), (x^2, moments(cref))]
+        @test μ isa AbstractMeasure{Float64}
+        @test length(moments(μ)) == 1
+        @test moment_value(moments(μ)[1]) ≈ 1.0 atol=atol rtol=rtol
+        @test monomial(moments(μ)[1]) == m
+    end
+
+    ν = moment_matrix(cref)
+    @test getmat(ν) ≈ ones(1, 1) atol=atol rtol=rtol
+    @test ν.x == [x]
+
+    S = SumOfSquares.SOSPolynomialSet{
+                                      SumOfSquares.typeof(set), typeof(cone), SumOfSquares.MonomialBasis,
+        Monomial{true},MonomialVector{true},Tuple{}
+    }
+    @test list_of_constraint_types(model) == [(Vector{JuMP.AffExpr}, S)]
+    test_delete_bridge(
+        model, cref, 1,
+        ((MOI.VectorOfVariables, MOI.Nonnegatives, 0),
+         (MOI.VectorAffineFunction{Float64},
+          SumOfSquares.PolyJuMP.ZeroPolynomialSet{
+              typeof(set), SumOfSquares.MonomialBasis,
+              Monomial{true}, MonomialVector{true}},
+          0)))
+end
+sos_term_fixed_test(optimizer, config)   = term_fixed_test(optimizer, config, SOSCone())
+sd_tests["sos_term_fixed"] = sos_term_fixed_test
+sdsos_term_fixed_test(optimizer, config) = term_fixed_test(optimizer, config, SDSOSCone())
+soc_tests["sdsos_term_fixed"] = sdsos_term_fixed_test
+dsos_term_fixed_test(optimizer, config)  = term_fixed_test(optimizer, config, DSOSCone())
+linear_tests["dsos_term_fixed"] = dsos_term_fixed_test