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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

New parallel descent-like method for solving a class of variational inequalitie

Language

English

Abstract

To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B. S. He in Comput. Optim. Appl. 42(2):195-212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data. © 2009 Springer Science+Business Media, LLC.

Keywords

Alternating direction methods, Augmented Lagrangian method, Descent-like methods, Parallel computing, Variational inequalities

Publication Date

2010

Source Publication Title

Journal of Optimization Theory and Applications

Volume

145

Issue

2

Start Page

311

End Page

323

Publisher

Springer Verlag

ISSN (print)

00223239

ISSN (electronic)

15732878

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