cvxopt is a different program than CVX. Ignore the cvxopt docuimentation if you want to use CVX.
You have provided the basic outline for CVX programs (there are some other optional things such as expressions). Just fill in the details for your problem per the CVX Users’ Guide and CVX examples, not cvxopt documentation.
Provide a primal or dual formulation, and CVX will handle it. If you have a semidefinite constraint, then specify it per the Users’ Guide ( == semidefinite(n) .or >= 0 if using sdp mode). Second order cone constraints can be entered in any way which follows CVX’s rules. CVX takes care of converting the problem into a standard form which the solvers can handle.