Help for solving an SDP problem


i’m trying to solve an SDP program using CVX for a long time but unfortunately i can not do that. your help will be appreciated because i don’t have much time to solve it:cry::cry::cry:

you can find my problem in attachment. also i can send my simulation code which i have generated all the data and matrices in it for anyone who wants to help. your helps is urgemtly needed. thanks in advance.

Is your first constraint convex? That hardly seems obvious. If so, how have you proven it so?

If it is not convex, perhaps you could employ CVX in an iterative manner, a la difference of convex functions. Move the denominator to the right-hand side and use the w_opt from the previous iteration in lieu of w on the left-hand side. You will need a starting value for w_opt for use on left-hand side, and will have no assurance that the CVX optimal solutions will converge at all, and if they do, that they will converge to the global or even a local optimum of your problem.

At the time of CVX invocation, is everything in the objective function and constraints known, with numerical values available in the MATLAB session, other than w?

as i said all matrices and values are known in my MTLAB session except W and min and max values of my constraints. with SDP relaxation it will be a convex problem. my main question is same, how i can use an iterative algorithm to solve this problem.

I’m not sure what your SDP relaxation is. But I gave you suggested approach to call CVX inside a for loop, per the 2nd paragraph in my post above. You will need an initial value of w_opt. And you will need a termination criterion to terminate out of the for loop.