Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 112, Issue 1, Pages 111-128Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1013096613105
Keywords
monotone variational inequalities; explicit methods; implicit methods; prediction-correction methods
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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.
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