Use WeightedSOSCone by default

.github/workflows/ci.yml

@@ -37,8 +37,13 @@ jobs:
         run: |
           using Pkg
           Pkg.add([
-              PackageSpec(name="MultivariateBases", rev="master"),
-              PackageSpec(name="MathOptInterface", rev="master"),
+              PackageSpec(name="MathOptInterface", rev="bl/set_map_type"),
+              PackageSpec(name="StarAlgebras", rev="bl/sos"),
+              PackageSpec(name="SymbolicWedderburn", rev="mk/StarAlgebras_0_3"),
+              PackageSpec(name="MultivariateBases", rev="bl/sos"),
+              PackageSpec(name="SemialgebraicSets", rev="master"),
+              PackageSpec(name="MultivariateMoments", rev="master"),
+              PackageSpec(name="PolyJuMP", rev="master"),
           ])
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1

.github/workflows/documentation.yml

@@ -22,6 +22,13 @@ jobs:
         run: |
           using Pkg
           Pkg.add([
+              PackageSpec(name="MathOptInterface", rev="bl/set_map_type"),
+              PackageSpec(name="StarAlgebras", rev="bl/sos"),
+              PackageSpec(name="SymbolicWedderburn", rev="mk/StarAlgebras_0_3"),
+              PackageSpec(name="MultivariateBases", rev="bl/sos"),
+              PackageSpec(name="SemialgebraicSets", rev="master"),
+              PackageSpec(name="MultivariateMoments", rev="master"),
+              PackageSpec(name="PolyJuMP", rev="master"),
               PackageSpec(path=pwd()),
           ])
           Pkg.instantiate()

.github/workflows/examples.yml

@@ -17,6 +17,13 @@ jobs:
         run: |
           using Pkg
           Pkg.add([
+              PackageSpec(name="MathOptInterface", rev="bl/set_map_type"),
+              PackageSpec(name="StarAlgebras", rev="bl/sos"),
+              PackageSpec(name="SymbolicWedderburn", rev="mk/StarAlgebras_0_3"),
+              PackageSpec(name="MultivariateBases", rev="bl/sos"),
+              PackageSpec(name="SemialgebraicSets", rev="master"),
+              PackageSpec(name="MultivariateMoments", rev="master"),
+              PackageSpec(name="PolyJuMP", rev="master"),
               PackageSpec(path=pwd()),
           ])
           Pkg.instantiate()

Project.toml

@@ -16,6 +16,7 @@ PolyJuMP = "ddf597a6-d67e-5340-b84c-e37d84115374"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SemialgebraicSets = "8e049039-38e8-557d-ae3a-bc521ccf6204"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+StarAlgebras = "0c0c59c1-dc5f-42e9-9a8b-b5dc384a6cd1"
 SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
 
 [compat]
@@ -29,5 +30,5 @@ MutableArithmetics = "1"
 PolyJuMP = "0.7"
 Reexport = "0.2, 1.0"
 SemialgebraicSets = "0.3"
-SymbolicWedderburn = "0.3"
+SymbolicWedderburn = "0.4"
 julia = "1.6"

bench/sos_polynomial.jl

@@ -5,7 +5,7 @@ function sos_polynomial(n)
     @polyvar x
     monos = monomials(x, 0:2n)
     set = SumOfSquares.SOSPolynomialSet(
-        SumOfSquares.FullSpace(), monos,
+        SumOfSquares.FullSpace(), MB.SubBasis{MB.Monomial}(monos),
         SumOfSquares.Certificate.Remainder(
             SumOfSquares.SOSCone(),
             SumOfSquares.MonomialBasis,

docs/src/constraints.md

@@ -153,7 +153,7 @@ where `α` and `β` are JuMP decision variables and `x` and `y` are polynomial
 variables. Since the polynomial is a quadratic form, the sum-of-squares
 certificate is also a quadratic form (see [Blekherman2012; Section~3.3.4](@cite)). Hence the
 default polynomial basis used for the [Nonnegative polynomial variables]
-certificate is `MonomialBasis([x, y])`, that is, we search for a positive
+certificate is `MultivariateBases.SubBasis{MultivariateBases.Monomial}([x, y])`, that is, we search for a positive
 semidefinite matrix `Q` such that
 ```math
 \alpha x^2 + \beta y^2 - (\alpha - \beta) x y = X^\top Q X
@@ -164,7 +164,7 @@ As the polynomial space is determined by the polynomial being constrained,
 only the basis *type* needs to be given. For instance, to use the scaled monomial
 basis in the example above, use
 ```jldoctest constraint-xy
-julia> @constraint(model, α * x^2 + β * y^2 ≥ (α - β) * x * y, basis = ScaledMonomialBasis)
+julia> @constraint(model, α * x^2 + β * y^2 ≥ (α - β) * x * y, basis = ScaledMonomial)
 (β)y² + (-α + β)xy + (α)x² is SOS
 ```
 

docs/src/tutorials/Extension/certificate.jl

@@ -53,10 +53,10 @@ solution_summary(model)
 import MultivariateBases as MB
 const SOS = SumOfSquares
 const SOSC = SOS.Certificate
-struct Schmüdgen{IC <: SOSC.AbstractIdealCertificate, CT <: SOS.SOSLikeCone, BT <: SOS.AbstractPolynomialBasis} <: SOSC.AbstractPreorderCertificate
+struct Schmüdgen{IC<:SOSC.AbstractIdealCertificate,CT<:SOS.SOSLikeCone,B<:SA.AbstractBasis} <: SOSC.AbstractPreorderCertificate
     ideal_certificate::IC
     cone::CT
-    basis::Type{BT}
+    basis::B
     maxdegree::Int
 end
 
@@ -78,8 +78,8 @@ function SOSC.multiplier_basis(certificate::Schmüdgen, index::SOSC.PreorderInde
     q = SOSC.generator(certificate, index, domain)
     return SOSC.maxdegree_gram_basis(certificate.basis, variables(domain), SOSC.multiplier_maxdegree(certificate.maxdegree, q))
 end
-function SOSC.multiplier_basis_type(::Type{Schmüdgen{IC, CT, BT}}) where {IC, CT, BT}
-    return BT
+function SOSC.multiplier_basis_type(::Type{Schmüdgen{IC, CT, BT}}, ::Type{M}) where {IC,CT,BT,M}
+    return MB.similar_type(BT, M)
 end
 
 function SOSC.generator(::Schmüdgen, index::SOSC.PreorderIndex, domain::SOSC.WithVariables)

src/Bridges/Bridges.jl

@@ -1,6 +1,36 @@
 module Bridges
 
+import MathOptInterface as MOI
+import SumOfSquares as SOS
+
 include("Variable/Variable.jl")
 include("Constraint/Constraint.jl")
 
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::Union{
+        SOS.GramMatrixAttribute,
+        SOS.MomentMatrixAttribute,
+        SOS.SOSDecompositionAttribute,
+    },
+    bridge::MOI.Bridges.Constraint.VectorSlackBridge,
+)
+    return MOI.get(model, attr, bridge.slack_in_set)
+end
+
+# TODO bridges should redirect to `MOI.get_fallback` as well so that
+# we can just use `Union{MOI.ConstraintIndex,MOI.Bridges.AbstractBridge}` in the `get_fallback` in `attributes.jl`
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::SOS.SOSDecompositionAttribute,
+    bridge::Union{
+        Variable.KernelBridge,
+        Constraint.ImageBridge,
+        Constraint.SOSPolynomialInSemialgebraicSetBridge,
+    },
+)
+    gram = MOI.get(model, SOS.GramMatrixAttribute(attr.result_index), bridge)
+    return SOS.SOSDecomposition(gram, attr.ranktol, attr.dec)
+end
+
 end

src/Bridges/Constraint/Constraint.jl

@@ -3,6 +3,7 @@ module Constraint
 using LinearAlgebra
 
 import MutableArithmetics as MA
+import StarAlgebras as SA
 
 import MathOptInterface as MOI
 
@@ -26,19 +27,4 @@ include("image.jl")
 include("sos_polynomial.jl")
 include("sos_polynomial_in_semialgebraic_set.jl")
 
-# TODO bridges should redirect to `MOI.get_fallback` as well so that
-# we can just use `Union{MOI.ConstraintIndex,MOI.Bridges.AbstractBridge}` in the `get_fallback` in `attributes.jl`
-function MOI.get(
-    model::MOI.ModelLike,
-    attr::SOS.SOSDecompositionAttribute,
-    bridge::Union{
-        ImageBridge,
-        SOSPolynomialBridge,
-        SOSPolynomialInSemialgebraicSetBridge,
-    },
-)
-    gram = MOI.get(model, SOS.GramMatrixAttribute(attr.result_index), bridge)
-    return SOS.SOSDecomposition(gram, attr.ranktol, attr.dec)
-end
-
 end

src/Bridges/Constraint/image.jl

@@ -119,9 +119,8 @@ function MOI.Bridges.Constraint.bridge_constraint(
                     MOI.Utilities.operate_output_index!(-, T, k, f, var)
                 else
                     found[mono] = k
-                    t = MP.searchsortedfirst(set.basis.monomials, mono)
-                    if t in eachindex(set.basis.monomials) &&
-                       set.basis.monomials[t] == mono
+                    t = MB.monomial_index(set.basis, mono)
+                    if !isnothing(t)
                         first[t] = k
                         if is_diag
                             MOI.Utilities.operate_output_index!(
@@ -168,7 +167,13 @@ end
 function MOI.supports_constraint(
     ::Type{ImageBridge{T}},
     ::Type{<:MOI.AbstractVectorFunction},
-    ::Type{<:SOS.WeightedSOSCone{M,<:MB.MonomialBasis,<:MB.MonomialBasis}},
+    ::Type{
+        <:SOS.WeightedSOSCone{
+            M,
+            <:MB.SubBasis{MB.Monomial},
+            <:MB.SubBasis{MB.Monomial},
+        },
+    },
 ) where {T,M}
     return true
 end