Epsilon-proximal decomposition method
type: Item
instance of: scholarly article
title: Epsilon-proximal decomposition method
zbMATH Open document ID: 1082.90088
author: Adam Ouorou
published in: Mathematical Programming. Series A. Series B
publication date: 2004-03-11T00:00:00Z
review text: The paper is concerned with a modification of a proximal decomposition method for minimizing a convex function over a subspace of \(\mathbb R^n\). In order to obtain a numerically suitable quadratic problem, which provides an approximation for the proximal step, the proximal decomposition method is combined with a bundle strategy. The resulting algorithmic scheme fits the general framework of Rockafellar's inexact proximal-point algorithm. Next a practical algorithm is developed which is based on recent ideas by \textit{M.V. Solodov} and \textit{B.F. Svaiter} [Set-Valued Analysis 7, 323--345 (1999; Zbl 0959.90038)]. It turns out that the approach is particularly useful when the objective function is a sum of convex functions. In that case, the quadratic subproblem in the algorithm splits into a number of smaller quadratic problems which, via parallel solution, could make the approach attractive for large-scale problems. Examples considered are a new stabilized version of Benders decomposition method and nonlinear convex multicommodity flow problems.
reviewed by: Rembert Reemtsen
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C59
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 2055183
zbMATH Keywords: convex optimization
zbMATH Keywords: proximal point algorithms
zbMATH Keywords: cutting planes
zbMATH Keywords: decomposition
zbMATH Keywords: multicommodity flows
zbMATH Keywords: large-scale programming
MaRDI profile type: Publication
full work available at URL: s10107-003-0371-0
OpenAlex ID: W2036987405
DOI: 10.1007/S10107-003-0371-0
description: scientific article; zbMATH DE number 2055183