An improved general extra-gradient method with refined step size for nonlinear monotone variational inequalities |
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Authors: | M H Xu X M Yuan Q L Huang |
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Institution: | (1) Department of Mathematics, Nanjing University, Jiangsu Province, 210093, China;(2) Department of Management Science, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, 200052, China;(3) Department of Information Science, Jiangsu Polytechnic University, Changzhou, Jiangsu Province, 213164, China |
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Abstract: | Extra-gradient method and its modified versions are direct methods for variational inequalities VI(Ω, F) that only need to use the value of function F in the iterative processes. This property makes the type of extra-gradient methods very practical for some variational inequalities
arising from the real-world, in which the function F usually does not have any explicit expression and only its value can be observed and/or evaluated for given variable. Generally,
such observation and/or evaluation may be obtained via some costly experiments. Based on this view of point, reducing the
times of observing the value of function F in those methods is meaningful in practice. In this paper, a new strategy for computing step size is proposed in general
extra-gradient method. With the new step size strategy, the general extra-gradient method needs to cost a relatively minor
amount of computation to obtain a new step size, and can achieve the purpose of saving the amount of computing the value of
F in solving VI(Ω, F). Further, the convergence analysis of the new algorithm and the properties related to the step size strategy are also discussed
in this paper. Numerical experiments are given and show that the amount of computing the value of function F in solving VI(Ω, F) can be saved about 12–25% by the new general extra-gradient method. |
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Keywords: | Nonlinear monotone variational inequality Extra-gradient method Prediction-correction method Projection contraction method |
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