Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities |
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Authors: | Bingsheng He Xiaoming Yuan Jason JZ Zhang |
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Institution: | (1) Department of Mathematics, Nanjing University, Nanjing, 210093, People's Republic of China;(2) Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong |
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Abstract: | In this paper, we study the relationship between the forward-backward splitting method and the extra-gradient method for monotone variational inequalities. Both of the methods can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. Our analysis explains theoretically why the extra-gradient methods usually outperform the forward-backward splitting methods. We suggest some modifications for the two methods and numerical results are given to verify the superiority of the modified methods. |
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Keywords: | Monotone variational inequalities forward-backward splitting methods extra-gradient methods prediction-correction methods |
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