Suppose that we use the DCP ruleset of CVX to solve a convex program (which can be equivalently written as a SOCP). After CVX parses the problem, does it automatically recognize that the given problem is in fact an SOCP? Is it possible to use the parsing capabilities of CVX to obtain the standard form of the problem? To elaborate, will we be able to extract the matrices \mathbf{A}_i and \mathbf{F}, vectors \mathbf{f}, \mathbf{b}_i, \mathbf{c}_i, and \mathbf{g}, and the numbers d_i in the following standard form SOCP:
\begin{eqnarray}
&\text{minimize} \quad &\mathbf{f}^T \mathbf{x} \
&\text{subject to} \quad &||\mathbf{A}_i \mathbf{x} + \mathbf{b}_i ||_2 \le \mathbf{c}_i^T \mathbf{x} + d_i, : i=1, \ldots, m, \
&&\mathbf{F}\mathbf{x}=\mathbf{g}.
\end{eqnarray}
** Update: I have used the standard form of the SOCP given in the book “Convex Optimization” by Professors Boyd and Vandenberghe.