Abstract. A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous, with Lipschitz constant no greater than 1. Virtually any subgradient method can be applied to solving the equivalent problem. The computational complexity ramifications are explored for a well-known "optimal" subgradient method.
Recently, Renegar REF presented a framework of applying gradient methods to general conic optimization problems by transforming original problem into an equivalent convex optimization problem with only linear equality constraints and Lipschitz continuous objective function.
A Framework for Applying Subgradient Methods to Conic Optimization Problems
arXiv: Optimization and Control
Mathematics