An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function.

In this work we aim to solve a convex-concave saddle point problem, where the convex-concave coupling function is smooth in one variable and nonsmooth in the other and assumed to be linear in either. The problem is augmented by a nonsmooth regulariser in the smooth component. We propose and investigate a novel algorithm under the name of , consisting of an step in the smooth variable coupled with a proximal step of the regulariser, and which is alternated with a in the nonsmooth component of the coupling function.