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期刊论文
Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities1
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 112, No.1, pp. 111-128, January 2002,-0001,():
In this paper, we study the relationship of some projectiontype 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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