Improvements of some projection methods for monotone nonlinear variational inequalities

  • Authors:

  • B. S. He;L. Z. Liao

  • Affiliations:

  • Professor, Department of Mathematics, Nanjing University, Nanjing, China;Associate Professor, Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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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.