When I tried to solve one problem whose objective includes pow_pos function, it always changes the solver to SDPT even I choose Mosek in Matlab. Why the solver changes automatically? Can I use Mosek or Sedumi to solve this problem?
Why the solver changes automatically?
This should not happen if you are using CVX properly. It is either user error or a bug. What happens if you put cvx_solver mosek immediately after cvx_begin?
Good! For now you should do that, then. If you wish to submit a bug report to http://support.cvxr.com, with the precise model that gives you problems, feel free to do so.