I have a problem consisting of both polynomial constraints (using the `PolyJuMP`

), with nonnegativity requirements on a certain domain, which should be able to be handled using the `SumOfSquares`

package and several second-order conic constraints. In short, I am having trouble including all the constraints and finding a solver to recognize the structure and start working. Specifically, I create two polynomial variables and both a nonnegativity and SOC constraint:

```
using JuMP
using PolyJuMP
using LinearAlgebra
using SumOfSquares
using DynamicPolynomials
model = SOSModel(CSDP.Optimizer)
# Variables
@polyvar xvar yvar
X = monomials([x, y], 0:2)
poly = @variable(model, poly, Poly(X))
domain = @set yvar == 1
# Nonnegativity constraint on domain
@constraint(model, poly >= 0, domain = domain)
poly_dx = differentiate(poly, xvar)
poly_dy = differentiate(poly, yvar)
poly_dx_val = poly_dx(1, 1)
poly_dy_val = poly_dy(1, 1)
term_val = norm([1; poly_dx_val; poly_dy_val])
obj_var = @variable(model, obj_var)
# SOC constraint
@constraint(model, obj_var >= term_val)
@objective(model, Min, obj_var)
```

However, I get a

```
LoadError: MathOptInterface.UnsupportedNonlinearOperator: The nonlinear operator `:norm` is not supported by the model.
```

As an alternative, I made the constraint more explicit:

```
term_val_sq = 1 + (poly_dx_val)^2 + (poly_dy_val)^2
@constraint(model, 0 >= term_val_sq - (obj_var^2))
@constraint(model, obj_var >= 0)
```

In that case I get the error

```
ERROR: LoadError: MathOptInterface.UnsupportedConstraint{MathOptInterface.ScalarQuadraticFunction{Float64}, MathOptInterface.GreaterThan{Float64}}: `MathOptInterface.ScalarQuadraticFunction{Float64}`-in-`MathOptInterface.GreaterThan{Float64}` constraint is not supported by the model: Unable to transform a quadratic constraint into a second-order
cone constraint because the quadratic constraint is not strongly convex.
```

even though the constraint should be convex. Any ideas on why I get these errors? Is there another optimizer backend which may work?