Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems

摘要

A generalization to the Rockafellar theorem (1976) on the linear convergence in the context of approximating a solution to a general class of inclusion problems involving set-valued A-maximal relaxed monotone mappings using the proximal point algorithm in a real Hilbert space setting is given. There exists a vast literature on this theorem, but most of the investigations are focused on relaxing the proximal point algorithm and applying it to the inclusion problems. The general framework for A-maximal relaxed monotonicity generalizes the theory of set-valued maximal monotone mappings, including H-maximal monotone mappings. The obtained results are general in nature, while application-oriented as well.