Convergence analysis of two-step inertial Douglas-Rachford algorithm and application

作     者：Dixit, Avinash Sahu, D. R. Gautam, Pankaj Som, T. 

作者机构：Indian Inst Technol BHU Dept Math Sci Varanasi Uttar Pradesh India Banaras Hindu Univ Inst Sci Dept Math Varanasi Uttar Pradesh India 

出 版 物：《JOURNAL OF APPLIED MATHEMATICS AND COMPUTING》 (国际应用数学与计算杂志)

年 卷 期：2022年第68卷第2期

页      面：953-977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：IIT(BHU) UGC, India 

主　　题：Inertial splitting algorithm Normal S-iteration method Douglas-Rachford splitting method Composite minimization problems Clustering problems 

摘      要：Monotone inclusion problems are crucial to solve engineering problems and problems arising in different branches of science. In this paper, we propose a novel two-step inertial Douglas-Rachford algorithm to solve the monotone inclusion problem of the sum of two maximally monotone operators based on the normal S-iteration method (Sahu, D.R.: Applications of the S-iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory 12(1), 187-204 (2011)). We have studied the convergence behavior of the proposed algorithm. Based on the proposed method, we develop an inertial primal-dual algorithm to solve highly structured monotone inclusions containing the mixtures of linearly composed and parallel-sum type operators. Finally, we apply the proposed inertial primal-dual algorithm to solve a highly structured minimization problem. We also perform a numerical experiment to solve the generalized Heron problem and compare the performance of the proposed inertial primal-dual algorithm to already known algorithms.