An accelerated inexact proximal point method for solving nonconvex-concave min-max problems

Abstract

This paper presents smoothing schemes for obtaining approximate stationary points of unconstrained or linearly-constrained composite nonconvex-concave min-max (and hence nonsmooth) problems by applying well-known algorithms to composite smooth approximations of the original problems. More specifically, in the unconstrained (resp. constrained) case, approximate stationary points of the original problem are obtained by applying, to its composite smooth approximation, an accelerated inexact proximal point (resp. quadratic penalty) method presented in a previous paper by the authors. Iteration complexity bounds for both smoothing schemes are also established. Finally, numerical results are given to demonstrate the efficiency of the unconstrained smoothing scheme.