I'm afraid this is not possible in the current version of CVX. The only thing I can think to do is dump out a copy of the raw solver data and run the solver by hand. To do that, type
help cvx_solver_settings at the MATLAB prompt, and examine the
Keep in mind, however, that nearly all solvers perform a variety of transformations on the problems they take in before they actually start the solution proper. In other words, in a very real way, the modeling process continues even once a solver (like SeDuMi) has been called. And of course, after the solution is obtained, the solver's transformations and CVX's must be reversed in order to get the desired answer.
So in a sense, the modeling process cannot be totally separated from the raw numerical method being employed.