An LS-free splitting method for composite mappings
type: Item
instance of: scholarly article
title: An LS-free splitting method for composite mappings
zbMATH Open document ID: 1092.49007
published in: Applied Mathematics Letters
publication date: 2006-01-24T00:00:00Z
review text: This paper gives a new splitting method for variational inclusion of the form \(0 \in A^TTA(x)\), where \(A\) is an \(m \times n \) matrix, \(T:R^m \rightrightarrows R^m\) is a maximal monotone mapping, and \(A^T\) denotes the transpose of \(A\). Compared with Pennanen's recently proposed method [\textit{T. Pennanen}, Numer. Funct. Anal. Optimization 23, No.~7--8, 875--890 (2002; Zbl 1054.49022)], our new scheme is free of the least squares subproblem at each iteration. Its global convergence is proven under maximal monotonicity of \(T\) and the existence of a solution.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 5001480
zbMATH Keywords: maximal monotone mapping
zbMATH Keywords: composite mapping
zbMATH Keywords: splitting method
zbMATH Keywords: least squares
author: Yunda Dong
reviewed by: Zhang Xian
MaRDI profile type: Publication
full work available at URL: j.aml.2004.09.013
OpenAlex ID: W2008994546
cites work: A SPLITTING METHOD FOR COMPOSITE MAPPINGS
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: Solving a class of linear projection equations
cites work: Modified Projection-Type Methods for Monotone Variational Inequalities
cites work: Variational Analysis
cites work: Partial inverse of a monotone operator
DOI: 10.1016/J.AML.2004.09.013
description: scientific article; zbMATH DE number 5001480