Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures

Language

English

Abstract

Splitting methods have been extensively studied in the context of convex programming and variational inequalities with separable structures. Recently, a parallel splitting method based on the augmented Lagrangian method (abbreviated as PSALM) was proposed in He (Comput. Optim. Appl. 42:195-212, 2009) for solving variational inequalities with separable structures. In this paper, we propose the inexact version of the PSALM approach, which solves the resulting subproblems of PSALM approximately by an inexact proximal point method. For the inexact PSALM, the resulting proximal subproblems have closed-form solutions when the proximal parameters and inexact terms are chosen appropriately. We show the efficiency of the inexact PSALM numerically by some preliminary numerical experiments. © 2011 Springer Science+Business Media, LLC.

Keywords

Augmented Lagrangian method, Parallel method, Prediction-correction method, Proximal point method, Splitting method, Variational inequalities

Publication Date

2012

Source Publication Title

Computational Optimization and Applications

Volume

52

Issue

2

Start Page

439

End Page

461

Publisher

Springer Verlag

DOI

10.1007/s10589-011-9417-z

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10589-011-9417-z

ISSN (print)

09266003

ISSN (electronic)

15732894

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