Two parallel distribution algorithms for convex constrained minimization problems
type: Item
instance of: scholarly article
title: Two parallel distribution algorithms for convex constrained minimization problems
zbMATH Open document ID: 1118.65064
author: Jie Shen
author: Wei Wang
author: Li-Ping Pang
published in: Applied Mathematics and Computation
publication date: 2007-06-06T00:00:00Z
review text: The aim of this paper is to study problems, whose objective functions are convex. A nonsmooth constrained parallel gradient distribution (PGD) algorithm is constructed based on a technique due to \textit{Y. R. He} [J. Optimization Theory Appl. 111, 137--153 (2001; Zbl 0987.90067)] where directions and stepsizes in subproblems are obtained via a certain method of solving quadratic programming and the procedure of Armijio type. This algorithm is similar in spirit to the classical block Jacobi and coordinate descent methods. Main result: The PGD algorithm is significantly different from those methods in that each subproblem in the parallelization phase needs to be solved only approximately, for example, by executing a single descent iteration. In a parallel variable distribution (PVD) algorithm, the variables are distributed among processors, each processor not only has primary responsibility for updating its own block of variables but also allows the other secondary variables to change in a restricted manner. A nonsmooth inexact PVD algorithm, in which the solutions of subproblems in the parallel step of the algorithm need not necessarily to be exact is proposed. The authors establish the convergence of this algorithm under some assumptions.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 5162031
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: parallel algorithm
zbMATH Keywords: convex programming
zbMATH Keywords: Moreau-Yosida regularization
zbMATH Keywords: convergence
zbMATH Keywords: parallel gradient distribution algorithm
zbMATH Keywords: coordinate descent methods
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.167
OpenAlex ID: W2011453618
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DOI: 10.1016/J.AMC.2006.08.167
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description: scientific article; zbMATH DE number 5162031