Forward-Backward Splitting with Bregman Distances

作     者：Quang Van Nguyen 

作者机构：Hanoi Natl Univ Educ Dept Math 136 Xuan Thuy St Hanoi Vietnam Ecole Polytech Fed Lausanne Lab Informat Theory & Inference Syst LIONS Lausanne Switzerland 

出 版 物：《VIETNAM JOURNAL OF MATHEMATICS》 (越南数学杂志)

年 卷 期：2017年第45卷第3期

页      面：519-539页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Banach space Bregman distance Forward-backward algorithm Legendre function Multivariate minimization Variable quasi-Bregman monotonicity 

摘      要：We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.