Improvements of some projection methods for monotone nonlinear variational inequalities

B. S. He, Lizhi LIAO

Research output: Contribution to journalArticlepeer-review

176 Citations (Scopus)

Abstract

In this paper, we study the relationship of some projection-type methods for monotone nonlinear variational inequalities and investigate some improvements. If we refer to the Goldstein-Levitin-Polyak projection method as the explicit method, then the proximal point method is the corresponding implicit method. Consequently, the Korpelevich extragradient method can be viewed as a prediction-correction method, which uses the explicit method in the prediction step and the implicit method in the correction step. Based on the analysis in this paper, we propose a modified prediction-correction method by using better prediction and correction stepsizes. Preliminary numerical experiments indicate that the improvements are significant.

Original languageEnglish
Pages (from-to)111-128
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume112
Issue number1
DOIs
Publication statusPublished - Jan 2002

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • explicit methods
  • implicit methods
  • Monotone variational inequalities
  • prediction-correction methods

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