Hi, I’m trying to get the optimal solution of a polynomial optimization problem by calculating the dual.

```
# Create symbolic variables (not JuMP decision variables)
@polyvar x1 x2
# Create a Sum of Squares JuMP model with the Mosek solver
model = SOSModel(with_optimizer(Mosek.Optimizer))
# Create a JuMP decision variable for the lower bound
@variable(model, γ)
# @variable(model, x)
# f(x) is the Goldstein-Price function
f1 = x1+x2+1
f2 = 19-14*x1+3*x1^2-14*x2+6*x1*x2+3*x2^2
f3 = 2*x1-3*x2
f4 = 18-32*x1+12*x1^2+48*x2-36*x1*x2+27*x2^2
f = (1+f1^2*f2)*(30+f3^2*f4)
@constraint(model, constr, f >= γ)
@objective(model, Max, γ)
optimize!(model)
```

The problem is successfully solved to optimal. The optimal objective value can be evaluated by

```
println(objective_value(model))
value(γ)
3.0000000209530935
```

When I tried to evaluate the optimal solution

```
ν3 = moment_matrix(constr)
extractatoms(ν3,1e-3)
```

and I got

Atomic measure on the variables x1, x2 with 1 atoms:

at [0.0, 0.0] with weight 0.9999999999872671

However, it is not the optimal solution since its corresponding objective value is 600.

```
subs(f, x1=>0, x2=>0)
600
```

I also check

```
MultivariateMoments.computesupport!(ν3, 1e-3)
```

and get

```
Algebraic Set defined by 12 equalities
-x2 = 0
-x1 = 0
-x2^2 = 0
-x1*x2 = 0
-x1^2 = 0
-x2^3 = 0
-x1*x2^2 = 0
-x1^2*x2 = 0
-x1^3 = 0
-x1^2*x2^2 + 0.49988336573392234*x1*x2^3 + 1.4998072823025776*x2^4 = 0
-x1^3*x2 + 1.7498451395778885*x1*x2^3 + 0.7496347168248607*x2^4 = 0
-x1^4 + 1.6244349952561488*x1*x2^3 + 2.6243893730401324*x2^4 = 0
```

while clearly, the true optimal solution (0,-1) does not satisfy these constraints.

Can anyone help me? Thanks in advance!