I am trying to model this optimization problem into cvx. Due to my limited knowledge i am struggling. can someone help me model in cvx. Any resources will be helpful. I don’t use matlab optimization toolbox.

I can’t read that image very clearly. Does the objective function have products of optimization variables t_i and \gamma_j? If so, that is a non-convex quadratic (not a Linear Program); so this would be a non-convex QP, and CVX can’;t be used. This could be handled in YALMIP.

if this really is a Linear Program, it would be straightforward to enter in CVX, presuming you’ve read the CVX Users’ Guide.

Yes, the variable t_i and gamma_i, are a product. The gamma is the SNR and t_i is the relaxation variable. because it is a NP hard problem. How can I prove it is a non-convex ?

if you evaluate the Hessian, you’ll see it is non-convex. CVX is not the right tool for this problem. Consider using YALMIP.