On compositions of special cases of Lipschitz continuous operators

Fixed Point Theory and Algorithms for Sciences and Engineering

Pontus Giselsson¹  Walaa M. Moursi² 

[1] Department of Automatic Control, Lund University;Department of Combinatorics and Optimization, University of Waterloo;

关键词: Compositions of operators;    Conically nonexpansive operators;    Douglas–Rachford algorithm;    Forward-backward algorithm;    Hypoconvex function;    Maximally monotone operator;   

DOI  :  10.1186/s13663-021-00709-0

来源: DOAJ

【 摘 要 】

Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.

【 授权许可】

Unknown