Convergence and Stability Analysis of a Generalized Proximal Point Algorithm and Its Inexact Version

Abstract

In this paper, we introduce the notion of adaptive strong monotonicity and establish a linear convergence of the recently proposed Generalized Proximal Point Algorithm (GPPA) for computing approximate solutions to nonmonotone inclusion problems in Hilbert spaces. We also investigate the Inexact Generalized Proximal Point Algorithm (IGPPA) in the presence of nondiminishing errors.