A Logarithmic-Quadratic Proximal Prediction-Correction Method for Structured Monotone Variational Inequalities

Authors:
Bing-Sheng He;Ya Xu;Xiao-Ming Yuan
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, China 210093;Department of Mathematics, Nanjing University, Nanjing, China 210093;Department of Mathematics, City University of Hong Kong, Hong Kong, China
Venue:
Computational Optimization and Applications
Year:
2006

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Abstract

Inspired by the Logarithmic-Quadratic Proximal (LQP) method for variational inequalities, we present a prediction-correction method for structured monotone variational inequalities. Each iteration of the new method consists of a prediction and a correction. Both the predictor and the corrector are obtained easily with tiny computational load. In particular, the LQP system that appears in the prediction is approximately solved under significantly relaxed inexactness restriction. Global convergence of the new method is proved under mild assumptions. In addition, we present a self-adaptive version of the new method that leads to easier implementations. Preliminary numerical experiments for traffic equilibrium problems indicate that the new method is effectively applicable in practice.