add __fast_recursive_dot to speed up constraints

src/sos_sdps.jl

@@ -160,6 +160,28 @@ sos_problem_primal(
     kwargs...
 ) = sos_problem_primal(elt, zero(elt), wedderburn; kwargs...)
 
+function __fast_recursive_dot!(
+    res::JuMP.AffExpr,
+    Ps::AbstractArray{<:AbstractMatrix{<:JuMP.VariableRef}},
+    Ms::AbstractArray{<:AbstractSparseMatrix};
+)
+    @assert length(Ps) == length(Ms)
+
+    for (A, P) in zip(Ms, Ps)
+        iszero(Ms) && continue
+        rows = rowvals(A)
+        vals = nonzeros(A)
+        for cidx in axes(A, 2)
+            for i in nzrange(A, cidx)
+                ridx = rows[i]
+                val = vals[i]
+                JuMP.add_to_expression!(res, P[ridx, cidx], val)
+            end
+        end
+    end
+    return res
+end
+
 function sos_problem_primal(
     elt::StarAlgebras.AlgebraElement,
     orderunit::StarAlgebras.AlgebraElement,
@@ -225,9 +247,9 @@ function sos_problem_primal(
         M_dot_P = sum(dot(M[π], P[π]) for π in eachindex(M) if !iszero(M[π]))
 
         if feasibility_problem
-            JuMP.@constraint(model, x == M_dot_P)
+            JuMP.@constraint(model, x == __fast_recursive_dot!(JuMP.AffExpr(), P, M))
         else
-            JuMP.@constraint(model, x - λ * u == M_dot_P)
+            JuMP.@constraint(model, x - λ * u == __fast_recursive_dot!(JuMP.AffExpr(), P, M))
         end
     end
     return model, P