New extragradient-type methods for solving variational inequalities

被引：4
作者：
Bnouhachem, Abdellah [1 ,2 ]
Fu, Xiao-Ling [3 ]
Xu, M. H. [4 ]
Sheng Zhaohan [1 ]
机构：
[1] Nanjing Univ, Sch Management Sci & Engn, Nanjing 210093, Peoples R China
[2] Ibn Zohr Univ, ENSA, Agadir, Morocco
[3] Nanjing SE Univ, Inst Syst Engn, Nanjing 210096, Peoples R China
[4] Jiangsu Polytech Univ, Sch Math & Phys, Changzhou 213164, Jiangsu Prov, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 216卷 / 08期
关键词：
Variational inequalities; Self-adaptive rules; Extragradient methods; Monotone operators; PROXIMAL POINT ALGORITHMS; CONVERGENT NEWTON METHOD; ITERATIVE METHODS; PROJECTION;
D O I：
10.1016/j.amc.2010.03.088
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose new methods for solving variational inequalities. The proposed methods can be viewed as a refinement and improvement of the method of He et al. [B. S. He, X. M. Yuan, J.J. Zhang, Comparison of two kinds of prediction-correction methods for monotone variational inequalities, Comp. Opt. Appl. 27 (2004) 247-267] by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. Under certain conditions, the global convergence of the both methods is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed methods. (C) 2010 Elsevier Inc. All rights reserved.
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页码：2430 / 2440
页数：11
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