Do you understand, i mean really understand what your optimization problem specification is? Because I don’t. I see symbols which I don’t know what they are.
What is E? Is that some kind of mathematical expectation, or some function? What is T? It is incumbent on you to tell us exactly what it is, and to determine whether F is a joint;y convex function of its arguments. Copying an image out of a paper or book of an optimization problem specification which you don’t understand, is not going to be a good way to learn optimization.
Start off by reading this Why isn't CVX accepting my model? READ THIS FIRST! . And the CVX Users’ Guide http://cvxr.com/cvx/doc/ . But I’m afraid that you will have to learn something about optimization first, and this forum is not he place to do that.And if F is not a joint;y convex function of its arguments, you will not be able to use CVX to solve this problem.