The Forward-Backward Algorithm and the Normal Problem

被引：7

作者：

Moursi, Walaa M. ^{[1
,2
]}

机构：

[1] Stanford Univ, Elect Engn, Stanford, CA 94305 USA

[2] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2018年 / 176卷 / 03期

关键词：

Attouch-Thera duality; Firmly nonexpansive mapping; Fixed point; Forward-backward splitting operator; Normal problem; MAXIMALLY MONOTONE-OPERATORS; SIGNAL RECOVERY; SUM; INCLUSIONS; PARAMONOTONICITY; DECOMPOSITION; CONVERGENCE; MAPPINGS; DUALITY; SPACE;

D O I：

10.1007/s10957-017-1113-4

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The forward-backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory.

引用

页码：605 / 624

页数：20

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