Convergence results of two-step inertial proximal point algorithm

作     者：Iyiola, Olaniyi S. Shehu, Yekini 

作者机构：Clarkson Univ Dept Math Potsdam NY USA Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Peoples R China 

出 版 物：《APPLIED NUMERICAL MATHEMATICS》 (应用数值数学)

年 卷 期：2022年第182卷

页      面：57-75页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The authors are grateful to the associate editor and the two anonymous referees for their insightful comments and suggestions which have improved greatly on the earlier version of the paper 

主　　题：Proximal point algorithm Two-point inertia Maximal monotone operators Weak and non-asymptotic convergence Hilbert spaces 

摘      要：This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O(1/n) convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.