From 295e21ad8d736b87f32f55bce4b43fec70dfd660 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Beno=C3=AEt=20Legat?= <benoit.legat@gmail.com>
Date: Wed, 10 Jul 2024 14:13:47 +0200
Subject: [PATCH] Add support for SumOfSquares cone

---
 Project.toml                  |  5 +++++
 src/Hypatia.jl                |  3 +++
 src/MathOptInterface/cones.jl | 19 +++++++++++++++++++
 3 files changed, 27 insertions(+)

diff --git a/Project.toml b/Project.toml
index 611e8e0b6..c6bdb38a4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,12 +11,17 @@ IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+MultivariateBases = "be282fd4-ad43-11e9-1d11-8bd9d7e43378"
+MultivariateMoments = "f4abf1af-0426-5881-a0da-e2f168889b5e"
 PolynomialRoots = "3a141323-8675-5d76-9d11-e1df1406c778"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+StarAlgebras = "0c0c59c1-dc5f-42e9-9a8b-b5dc384a6cd1"
 SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+SumOfSquares = "4b9e565b-77fc-50a5-a571-1244f986bda1"
+SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
diff --git a/src/Hypatia.jl b/src/Hypatia.jl
index 3b3f55d91..42c2fdf22 100644
--- a/src/Hypatia.jl
+++ b/src/Hypatia.jl
@@ -44,6 +44,9 @@ const VI = MOI.VariableIndex
 const SAF = MOI.ScalarAffineFunction
 const VV = MOI.VectorOfVariables
 const VAF = MOI.VectorAffineFunction
+import StarAlgebras
+import MultivariateBases
+import SumOfSquares
 include("MathOptInterface/cones.jl")
 include("MathOptInterface/transform.jl")
 include("MathOptInterface/wrapper.jl")
diff --git a/src/MathOptInterface/cones.jl b/src/MathOptInterface/cones.jl
index d4c67a35a..a1a84f1e4 100644
--- a/src/MathOptInterface/cones.jl
+++ b/src/MathOptInterface/cones.jl
@@ -635,6 +635,24 @@ function cone_from_moi(
     return Cones.WSOSInterpNonnegative{T, R}(cone.U, cone.Ps, use_dual = cone.use_dual)
 end
 
+function _transformation_to(lag::MultivariateBases.LagrangeBasis, gram, weight)
+    return StarAlgebras.coeffs(weight, lag) .* MultivariateBases.transformation_to(gram, lag)
+end
+
+function cone_from_moi(
+    ::Type{T},
+    cone::SumOfSquares.WeightedSOSCone{MOI.PositiveSemidefiniteConeTriangle,<:MultivariateBases.LagrangeBasis},
+) where {T<:Real}
+    return cone_from_moi(
+        T,
+        WSOSInterpNonnegativeCone{T,T}(
+            length(cone.basis),
+            _transformation_to.(Ref(cone.basis), cone.gram_bases, cone.weights),
+        ),
+    )
+end
+
+
 """
 $(TYPEDEF)
 
@@ -785,6 +803,7 @@ const SupportedCone{T <: Real} = Union{
     MOI.DualExponentialCone,
     MOI.LogDetConeTriangle,
     MOI.RelativeEntropyCone,
+    SumOfSquares.WeightedSOSCone{MOI.PositiveSemidefiniteConeTriangle,<:MultivariateBases.LagrangeBasis},
 }
 
 Base.copy(cone::HypatiaCones) = cone # maybe should deep copy the cone struct, but this is expensive