Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities

B. S. He and L. Z. Liao
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B. S. He: Nanjing University
L. Z. Liao: Hong Kong Baptist University

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 1, No 6, 128 pages

Abstract: 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.

Keywords: Monotone variational inequalities; explicit methods; implicit methods; prediction-correction methods (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (19)

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DOI: 10.1023/A:1013096613105

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