[1]漆林军,何诣然*.非单调型变分不等式问题的新双投影算法[J].四川师范大学学报(自然科学版),2020,43(04):463-468.[doi:10.3969/j.issn.1001-8395.2020.04.007]
 QI Linjun,HE Yiran.New Double Projection Algorithms for Non-monotone Variational Inequality Problems[J].Journal of SichuanNormal University,2020,43(04):463-468.[doi:10.3969/j.issn.1001-8395.2020.04.007]
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非单调型变分不等式问题的新双投影算法()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年04期
页码:
463-468
栏目:
基础理论
出版日期:
2020-06-20

文章信息/Info

Title:
New Double Projection Algorithms for Non-monotone Variational Inequality Problems
文章编号:
1001-8395(2020)04-0463-06
作者:
漆林军 何诣然*
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
QI Linjun HE Yiran
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
非单调型变分不等式 双投影算法 超平面
Keywords:
non-monotone variational inequalities double projection algorithm hyperplane
分类号:
O22; O177.92
DOI:
10.3969/j.issn.1001-8395.2020.04.007
文献标志码:
A
摘要:
投影算法作为一种求解变分不等式的简洁方法,常常要求所涉及的映射具有某种单调性,文献( M. Ye, Y. He. Computational Optimization and Applications,2015,60(1):141-150.)将双投影算法的标准单调性假设,用一个对偶变分不等式的解集非空的假设来替代,提出了一种新的算法,并建立了其全局收敛性.在此基础上,选取不同的超平面,提出新的算法.在对偶变分不等式问题的解集非空的假设下,建立其全局收敛性,并给出数值实验结果.
Abstract:
As an effective method to solve variational inequalities, the projection algorithm usually requires that the underlying mapping satisfies some monotone-type conditions. Recently,(M. Ye, Y. He. Computational Optimization and Applications, 2015, 60(1):141-150.)uses the assumption that the solution set of the dual variational inequality problem is nonempty to replace the standard monotonicity assumption of the underlying mapping, gives a double projection algorithm, and establishes its global convergence. In this paper, we propose new algorithms with a strategy for selecting new hyperplanes. Under the same condition as Ye's, that is, the solution set of the dual variational inequality problem is nonempty, we prove the global convergence of the method. Numerical experiment results are reported.

参考文献/References:

[1] GOLDSTEIN A A. Convex programming in Hilbert space[J]. Bulletin of the American Mathematical Society,1964,70(5):709-710.
[2] LEVITIN E S, POLYAK B T. Constrained minimization problems[J]. USSR Computational Mathematical Physics,1966,6(5):1-50.
[3] FACCHINEI F, PANG J S. Finite-Dimensional Variational Inequalities and Complementarity Problems[M]. Berlin:Springer-Verleg,2003.
[4] KORPELEVICH G M. The extragradient method for finding saddle points and other problems[J]. Ekonomikai Matematicheskie Metody,1976,12(4):747-756.
[5] IUSEM A N, SVAITER B F. A variant of Korpelevich's method for variational inequalities with a new search strategy[J]. Optimization,1997,42(4):309-321.
[6] XIU N H, ZHANG J Z. Some recent advances in projection-type methods for variational inequalities [J]. Journal of Computational and Applied Mathematics,2003,152(1):559-585.
[7] YE M L, HE Y R. A double projection method for solving variational inequalities without monotonicity[J]. Computational Optimization and Applications,2015,60(1):141-150.
[8] FUKUSHIMA M. 非线性最优化基础[M]. 林贵华,译. 北京:科学出版社,2011.
[9] HE Y R. A new double projection algorithm for variational inequalities[J]. Journal of Computational and Applied Mathematics,2006,185(1):166-173.
[10] HADJISAVVAS N, SCHAIBLE S. Quasimonotone variational inequalities in Banach spaces[J]. Journal of Optimization Theory and Applications,1996,90(1):95-111.
[11] SUN D F. A new step-size skill for solving a class of nonlinear equations[J]. Journal of Computational Mathematics,1995,13(4):357-368.
[12] HARTMAN P, STAMPACCHINA G. On some non-linear elliptic differential-functional equations[J]. Acta Mathematica,1966,115(1):271-310.
[13] HARKER P T. Accelerating the convergence of the diagonalization and projection algorithms for finite-dimensional variational inequalities[J]. Mathematical Programming,1988,41(1):29-59.
[14] PANG J S, GABRIEL S A. NE/SQP:a robust algorithm for the nonlinear complementarity problem[J]. Mathematical Programming,1993,60(3):295-337.
[15] SOLODOV M V, SVAITER B F. A new projection method for variational inequality problems[J]. SIAM Journal on Control and Optimization,1999,37(3):765-776.

备注/Memo

备注/Memo:
收稿日期:2018-08-30 接受日期:2018-11-19
基金项目: 四川省科技厅项目(2018JY0201)
*通信作者简介:何诣然(1973—),男,教授,主要从事非线性最优化的研究,E-mail:yrhe@sicnu.edu.cn
更新日期/Last Update: 2020-06-20