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

Min Tao*, Xiaoming YUAN

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)439-461
Number of pages23
JournalComputational Optimization and Applications
Volume52
Issue number2
DOIs
Publication statusPublished - Jun 2012

Scopus Subject Areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

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

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