JuMP Empty Constraint when using SumOfSquares

Specific Domains Optimization (Mathematical)
1

Hello,

I’m trying to find some sum of squares representation for some polynomials, but I have been receiving some errors. Here is a shortened version of this code that gives this error:

using TypedPolynomials
using Combinatorics
using CSDP
using SumOfSquares

@polyvar a b
@polyvar x[1:2]

q = (a *x[1]+b*x[2])^2
Derb = subs(differentiate(q, b), a=> 1, b => -1)

solver = optimizer_with_attributes(CSDP.Optimizer)
model = SOSModel(solver)
@variable(model, c)
@constraint(model, cref, Derb in SOSCone())
@objective(model, Min, 0)
JuMP.optimize!(model)

This gives the error

ERROR: LoadError: ArgumentError: Empty constraint MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}[MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}(1), MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}(2)]: MathOptInterface.ScalarAffineFunction{Float64}(MathOptInterface.ScalarAffineTerm{Float64}[], 0.0)-in-MathOptInterface.EqualTo{Float64}(2.0). Not supported by CSDP.

What is the issue here? The actual polynomials I would like to prove are SOS are somewhat more complicated than this, but are also the derivatives of some other polynomials, with some variables then fixed to specific values.

Thanks - Kevin

1 Like
2

It looks like the issue is that SumOfSquares is trying to add a constraint like 0 == 2

@blegat is this expected?

3

This is because the Newton Polytope makes it trivial that this polynomial is not SOS. The degree in x1 is odd so it will be negative either at Info or -Inf

4

Yes, in the more complicated examples, something similar was happening. I would expect that this would immediately output “infeasible”, instead of this error. I will put in an issue on github.

5

This is an issue with CSDP then. A probable work-around is to use a different solver, like Mosek or SCS.

6

Yes, this is an issues with CSDP and it works with other solvers. I know this bug for a while but I’m not sure what’s the right fix without adding a lot of extra complexity either in CSDP or SumOfSquares. It’s usually a sign of incorrect modeling so I’ve always found the error actually helpful