Epigraph proximal algorithms for general convex programming

This work aims at partially bridging the gap between (generic but slow) “generalpurpose” convex solvers and (fast but constricted) “specialized” solvers. We develop the Epsilon system, a solver capable of handling general convex problems (inputs are specified directly as disciplined convex programs); however, instead of transforming these problems to cone form, the compiler transforms them to a higher-level “sum-of-prox” which can be solved via splitting methods, and which maintains significantly more problem structure. To make such transformations feasible for general convex problems, a key contribution is the development of efficient proximal and epigraph projection operators a wide range of convex functions. As we show, the resulting system improves substantially, often by an order of magnitude or more, over CVXPY combined with the splitting cone solver (SCS), a state-of-the art method for solving DCPs via their conic form.