The type of the optimization problem

[wang lingyi]

Dear Prof. Lofberg,

I am trying to solve the following optimization problem using mosek within yalmip in Matlab, but the solver turns out the message that

"Warning: Solver not applicable (mosek does not support multi-term monomial equalities)"

Why would this happens? And what type does the following optmization problem belong to? The matrix P in the following optimization problem is positive definite.

 Hope you can reply me. Thank you so much!

[Johan Löfberg]

your picture does not say it, but you have something like x^0.5+y*z == 1 or something like that (i'.e a nonlinear equality involving polynomials and/posynomials)

(49, 50) are nonconvex qp constraints, so already there you are ruling out mosek 

[wang lingyi]

Dear Prof. Lofberg,

Thank you for your reply. Since the optimization problem in the picture has nonconvex constraints, does the optimization problem belong to the nonconvex quadratically constrained quadratic program (QCQP)? Hope you can reply. Thank you so much!

[Johan Löfberg]

As I said, there are nonconvex quadratic inequalities clearly visible, but the error message indicates there are other nonconvexities too

[wang lingyi]

Dear Prof. Lofberg,

Thank you for your reply. For the above quadratic program which involves both convex and nonconvex quadratic inequalities, what solver should I choose？ Hope you can reply. Thank you so much.

[Johan Löfberg]

https://yalmip.github.io/tags/#nonconvex-quadratic-programming-solver

[wang lingyi]

Dear Prof. Lofberg,

Thank you for your reply. I installed the QUADPROGBB solver, and I tried to solve the above optimization problem. The yalmip gives me the message that "Warning: Solver not applicable (quadprogbb does not support nonconvex quadratic constraints). Can you give a hint that which solver in this link  https://yalmip.github.io/tags/#nonconvex-quadratic-programming-solver  can support to solve the optimization problem with nonconvex quadratic constraints? Thank you so much.

[Johan Löfberg]

gurobi (or simply built-in solver bmibnb)