A simple algorithm for a class of nonsmooth convex–concave saddle-point problems

We introduce a novel algorithm for solving a class of structured nonsmooth convex–concave saddle-point problems involving a smooth function and a sum of finitely many bilinear terms and nonsmooth functions. The proposed method is simple and proven to globally converge to a saddle-point with an O(1/ε)O(1/ε) efficiency estimate. We demonstrate its usefulness for tackling a broad class of minimization models with a finitely sum of composite nonsmooth functions.