I have a problem in which there are quadratic-over-linear terms in the objective function. All constraints are affine. I successfully implemented it in CVX and the results are satisfactory.
I was wondering why CVX implemented this problem as an SOCP? I understand that one can move the quadratic-over-linear terms from the objective function to a constraint and then convert it to a second-order cone constraint. Is there any particular reason for choosing this conversion over solving it as a general nonlinear and convex problem? Are SOCP solvers more efficient?
Maybe this problem fits more into the type of general optimization questions. In that case I apologize. It is however about a particular implementation in CVX, so I decided to try my luck here. Anyway, thank you!