Need help CVX with SCA

Hello,guys. I really need help. :sob: I have been trying to use cvx and SCA to solve the multi-user beamforming problem. The orignial problem is non-convex and SCA is adopted to transform it into convex. No matter how I modify my code, I can’t get the right result. The result of SCA does not increase but decrease. (NAN finally) Since the SINR is low, I scale it. (C5) is non-convex, I drop this rank-1 constraint by applying SDR.I really don’t know what can I do. I have been working on it for many days.

Here is the cvx running result.

here is the problem, W is the optimize variable.

Here is the specific item.

Here is SCA method to transform the nonm-convex problem.

Here is the overrall problem.

(C5) is non-convex, I drop this rank-1 constraint by applying SDR.

If anyone can help me, I would appreciate it very much!!!

You have a nonlinear SDP. That is a difficult non-convex optimization problem. You should consider ti a miracle if unsafeguarded SCA somehow worked on this problem. if you have good stating values, that might help. If the dimension of the problem is small enough, perhaps it can be solved by BMBNB under YALMIP develop version, or by use of FMINCON under YALMIP develop version (the latter being an experimental capability which may or may not work).

Unsafeguarded (no line search or trust region) SCA is unreliable. It might not descend (for minimization problem), i.e., iterates could get worse. It might not converge to anything; and if it does converge, it might not be to a local optimum of the original problem, let alone a global optimum. The solution of successive iterations, and therefore subproblem inputs, can become wilder and wilder, until at some point the solver fails, or makes erroneous determination of infeasibility or unboundedness.

Don’t apply crude, unsafeguarded (no Trust Region or Line Search) Successive Convex Approximation (SCA) to a new problem … unless your name happens to be Stephen Boyd.

There’s a reason high quality non-convex nonlinear optimization solvers are more than 10 lines long.