I have an optimization problem in CVX MATLAB:

min t

subject to

f(x) <= w^2*zeta + w*beta - t*w

w >= 0

trace(x) <= P,

where t, w, and x are optimization parameters, and beta and zeta are positive constant scalars. x has to be a complex semidefinite matrix and f(x) is a convex function of x. The product t*w makes the problem non-convex. How could I convexify the problem?