NEW DOUGLAS-RACHFORD ALGORITHMIC STRUCTURES AND THEIR CONVERGENCE ANALYSES

作     者：Censor, Yair Mansour, Rafiq 

作者机构：Univ Haifa Dept Math IL-3498838 Haifa Israel 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：2016年第26卷第1期

页      面：474-487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：United States-Israel Binational Science Foundation (BSF) 

主　　题：algorithmic structures convex feasibility problem string-averaging block-iterative firmly nonexpansive quasi-nonexpansive strictly Fejer monotone Douglas-Rachford strong convergence m-set-Douglas-Rachford operator 

摘      要：In this paper we study new algorithmic structures with Douglas-Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the string-averaging projections and into the block-iterative projection algorithmic structures, thereby creating new DR algorithmic schemes that include the recently proposed cyclic DR algorithm and the averaged DR algorithm as special cases. We further propose and investigate a new multiple-set-DR algorithmic operator. Convergence of all these algorithmic schemes is studied by using properties of strongly quasi-nonexpansive operators and firmly nonexpansive operators.