Can you specify cvx SDP and minimization in general to stop at a certain point in terms of accuracy or iterations?
Please read http://cvxr.com/cvx/doc/solver.html#controlling-precision
For the best control over what the solver does, you may set solver parameters or accuracy, maximum number of iterations, or anything else, using cvx_solver_settings as documented at http://cvxr.com/cvx/doc/solver.html#advanced-solver-settings