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?