Regularized HPE-Type Methods for Solving Monotone Inclusions with Improved Pointwise Iteration-Complexity Bounds

Abstract

This paper studies the iteration complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that the pointwise iteration complexity of the proposed methods considerably improves upon that of the HPE method while approaching (up to a logarithmic factor) the ergodic iteration complexity of the latter method.