Inexact alternating-direction-based contraction methods for separable linearly constrained convex optimization
type: Item
instance of: scholarly article
title: Inexact alternating-direction-based contraction methods for separable linearly constrained convex optimization
zbMATH Open document ID: 1322.90065
author: Guoyong Gu
author: Junfeng Yang
author: Bingsheng He
published in: Journal of Optimization Theory and Applications
publication date: 2014-11-03T00:00:00Z
review text: Let \(b\in \mathbb{R}^{m}\) and, for \(i=1,\dots,N\), let \(\theta _{i}:\mathbb{R}^{n_{i}}\rightarrow \mathbb{R}\) be a convex function, \(A_{i}\in \mathbb{R}^{m\times n_{i}}\), and \(\mathcal{X}_{i}\subseteq \mathbb{R}^{n_{i}}\) be a closed convex set. The problem under consideration consists in minimizing \(\sum\limits_{i=1}^{N}\theta _{i}(x_{i})\) subject to \(\sum\limits_{i=1}^{N}A_{i}x_{i}=b\) and \(x_{i}\in \mathcal{X}_{i}\) \((i=1,\dots,N)\). The authors present two modifications of the method proposed by the second author et al. [Optimization 62, No. 4, 573--596 (2013; Zbl 1273.90122)], which have the advantage that the subproblems are solved inexactly. Convergence results are obtained, and the rates of convergence are proved to be \(O(1/t)\).
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 6363603
zbMATH Keywords: alternating direction method
zbMATH Keywords: contraction method
zbMATH Keywords: convex optimization
zbMATH Keywords: convergence
zbMATH Keywords: complexity
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: s10957-013-0489-z
OpenAlex ID: W2012427950
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DOI: 10.1007/S10957-013-0489-Z
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description: scientific article; zbMATH DE number 6363603