Nonlinear Polynomial Optimization

[Asad]

I am trying to solve this constrained optimization problem using yalmip,

sdpvar x y gamma1;

p1 = (1+x*y)^2-x*y+(1-y)^2;

p2 =  x^2+y^2;

[S1,c1,v1] = polynomial([x y],2);

[S2,c2,v2] = polynomial([x y],2);

[S3,c3,v3] = polynomial([x y],2);

F =[sos(-S1*(gamma1-p1)- S2*(p2-10) - S3*(p2-100)*(gamma1-p1) - (p2-10)^2)];

solvesos(F,-gamma1,[],[gamma1;c1;c2;c3])

double(gamma1)

---I got this message when i ran it,

solvertime: 0

          info: 'No suitable solver'

       problem: -2

    yalmiptime: 0.7860

ans =

   NaN

After searching for the problem i came to know that i needed "SNOPT". I have downloaded it but i dont know how to use it in Yalmip?

asad

[Johan Löfberg]

You are multiplying decision variables (gamma1 and c1, etc), so you have a nonconvex semidefinite program. It is typically intractable. Sure local solverpenlab, and/or the global solver bmibnb built-in YALMIP "solves" polynomial SDPs, but the probability of this to work is very low.

You have to derive a linear SOS problem, or devise your own solution strategy (bisection in gamma1 would be pretty simple and would probably work fine)