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

Authors:
Min Tao;Xiaoming Yuan
Affiliations:
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China 210046;Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
Venue:
Computational Optimization and Applications
Year:
2012

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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.