[1]陈 园,何诣然*.求解伪单调型变分不等式的一种投影算法[J].四川师范大学学报(自然科学版),2020,43(03):297-303.[doi:10.3969/j.issn.1001-8395.2020.03.002]
 CHEN Yuan,HE Yiran.A Projection Algorithm for Solving Pseudomonotone Variational Inequalities[J].Journal of SichuanNormal University,2020,43(03):297-303.[doi:10.3969/j.issn.1001-8395.2020.03.002]
点击复制

求解伪单调型变分不等式的一种投影算法()
分享到:

《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03期
页码:
297-303
栏目:
基础理论
出版日期:
2020-05-05

文章信息/Info

Title:
A Projection Algorithm for Solving Pseudomonotone Variational Inequalities
文章编号:
1001-8395(2020)03-0297-07
作者:
陈 园 何诣然*
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
CHEN Yuan HE Yiran
School of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
变分不等式 投影算法 超平面
Keywords:
variational inequalities projection algorithm hyperplane
分类号:
O22; O177.92
DOI:
10.3969/j.issn.1001-8395.2020.03.002
文献标志码:
A
摘要:
在投影收缩算法的基础上,通过构造一种超平面,给出求解伪单调型变分不等式的一种投影算法,并证明该算法在变分不等式解集非空且F为伪单调连续映射的条件下是全局收敛的.在该算法生成的序列满足某种误差界条件下,得到算法的收敛率.最后,用数值实验对比所提算法与已知4种算法的收敛效果.
Abstract:
In this paper, based on projection and contraction method, we introduce a projection algorithm for solving pseudomonotone variational inequalities. If the solution of the varational inequality does exist and F is a continuous and pseudomonotone mapping, the sequence produced by our method globally converges to a solution. If a certain error bound holds, the convergence rate of the iterative sequence is established. Finally, numerical experiments are reported.

参考文献/References:

[1] HARKER P T, PANG J S. Finite-dimensional variational inequality and nonlinear complementarity problems:a survey of theory, algorithms and applications[J]. Math Program,1990,48(2):161-220.
[2] FACCHINEI F, PANG J S. Finite-dimensional Variational Inequalities and Complementarity Problems[M]. New York: Springer-Verlag,2003.
[3] SOLODOV M V, TSENG P. Modified projection-type methods for monotone variational inequalities[J]. SIAM J Control Optim,1996,34(5):1814-1830.
[4] SOLODOV M V, SVAITER B F. A new projection method for variational inequality problems[J]. SIAM J Control Optim,1999,37(3):765-776.
[5] WANG Y J, XIU N H, WANG C Y. A new version of extragradient method for variational inequality problems[J]. Comput Math Appl,2001,42(6):969-979.
[6] WANG Y J, XIU N H, WANG C Y. Unified framework of extragradient-type methods for pseudomonotone variational inequalities[J]. J Optim Theory Appl,2001,111(3):641-656.
[7] HE Y R. A new double projection algorithm for variational inequalities[J]. J Comput Appl Math,2006,185(1):166-173.
[8] LI F L, HE Y R. An algorithm for generalized variational inequality with pseudomonotone mapping[J]. J Comput Appl Math,2009,228(1):212-218.
[9] FANG C J, HE Y R. A double projection algorithm for multi-valued variational inequalities and a unified framework of the method[J]. Appl Math Comput,2011,217(23):9543-9551.
[10] LIN G H, ZHANG L W, PANG L P. Two projection-type algorithms for solving pseudomonotone variational inequality problem[J]. Arch Control Sci,2000,10(3):157-165.
[11] HE B S. A class of projection and contraction methods for monotone variational inequalities[J]. Appl Math Optim,1997,35(1):69-76.
[12] GAFNI E M, BETSEKAS D P. Two-metric projection methods for constrained optimization[J]. SIAM J Control Optim,1984,22(6):936-964.
[13] CAI X, GU G, HE B S. On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators[J]. Comput Optim Appl,2014,57(2):339-363.
[14] BNOUHACHEM A, FU X L, XU M H, SHENG Z H. New extragradient-type methods for solving variational inequalities[J]. Appl Math Comput,2010,216(8):2430-2440.
[15] DONG Q L, CHO Y J, RASSIA T M. The projection and contraction methods for finding common solutions to variational inequality problems[J]. Optim Lett,2018,12:1871-1896.
[16] DONG Q L, LU Y, YANG J. Approximately solving multi-valued variational inequalities by using a projection and contraction algorithm[J]. Numerical Algorithms,2017,76(3):799-812.
[17] BNOUHACHEM A, QAMRUL H A, WEN C F. A projection descent method for solving variational inequalities[J]. J Inequal Appl,2015,143(1):143-157.
[18] VERMA R U. A class of projection-contraction methods applied to monotone variational inequality[J]. Appl Math Lett,2000,13(8):55-62.
[19] DONG Q L, CHO Y J, ZHANG L L. Inertial projection and contraction algorithms for variational inequalities[J]. J Glob Optim,2018,70(3):687-704.

相似文献/References:

[1]艾艺红.混合变分不等式和非扩张映射解的迭代算法[J].四川师范大学学报(自然科学版),2012,(01):21.
 AI Yi hong.Iterative Methods for Mixed Variational Inequalities and Nonexpansive Mappings[J].Journal of SichuanNormal University,2012,(03):21.
[2]叶明露,邓方平,黄 穗.变分不等式的一类梯度投影算法[J].四川师范大学学报(自然科学版),2008,(01):43.
 YEM inglu,DENG Fangping,HUANG Sui.An ExtraˉgradientProjectionMethod for Classic Variational Inequality[J].Journal of SichuanNormal University,2008,(03):43.
[3]方长杰,田有先.一类带有三元算子的广义混合拟平衡问题[J].四川师范大学学报(自然科学版),2008,(03):285.
 FANG Changjie,TIAN Youxian.A Class ofGeneralizedM ixed Quasiˉequilibrium Problem with Trifunction[J].Journal of SichuanNormal University,2008,(03):285.
[4]刘智,何诣然*.集值变分不等式解的存在性问题[J].四川师范大学学报(自然科学版),2010,(02):156.
 LIU Zhi,HE Yi ran.An Existence of Solution to Setvalued Variational Inequalities[J].Journal of SichuanNormal University,2010,(03):156.
[5]何诣然.具有集值映射变分不等式的理论分析[J].四川师范大学学报(自然科学版),2010,(06):840.
 HE Yi ran.Theory on Variational Inequality Involved with Setvalued Mapping[J].Journal of SichuanNormal University,2010,(03):840.
[6]陈胜兰,方长杰.变分不等式的新超梯度迭代法[J].四川师范大学学报(自然科学版),2012,(01):12.
 CHEN Sheng lan,FANG Chang jie.A New Extragradient Iterative Method for Variational Iequalities[J].Journal of SichuanNormal University,2012,(03):12.
[7]常 菲.伪单调变分不等式近似点算法的收敛性[J].四川师范大学学报(自然科学版),2012,(04):439.
 CHANG Fei.Pseudomonotone Variational Inequalities: Convergence of Proximal Point Algorithm[J].Journal of SichuanNormal University,2012,(03):439.
[8]叶明露,邓方平.一般变分不等式的超梯度算法[J].四川师范大学学报(自然科学版),2005,(03):265.
 YE Ming-lu,DENG Fang-ping(College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2005,(03):265.
[9]方长杰,王 盈.Hilbert空间中变分不等式的一种新算法[J].四川师范大学学报(自然科学版),2015,(06):824.[doi:10.3969/j.issn.1001-8395.2015.06.006]
 FANG Changjie,WANG Ying.A New Algorithm for Variational Inequality Problems in a Hilbert Space[J].Journal of SichuanNormal University,2015,(03):824.[doi:10.3969/j.issn.1001-8395.2015.06.006]
[10]蒲思思,何诣然*.广义松弛拟单调映射以及广义松弛拟凸函数[J].四川师范大学学报(自然科学版),2016,(03):337.[doi:10.3969/j.issn.1001-8395.2016.03.007]
 PU Sisi,HE Yiran.Generalized Relaxed Quasimonotone Mappings and Generalized Relaxed Quasiconvex Functions[J].Journal of SichuanNormal University,2016,(03):337.[doi:10.3969/j.issn.1001-8395.2016.03.007]
[11]邱丹,邱涛,何诣然.一类二次投影算法的扰动分析[J].四川师范大学学报(自然科学版),2010,(06):741.
 QIU Dan,QIU Tao,HE Yi ran.A Kind of Perturbation Analysis of a Double Projection Algorithm[J].Journal of SichuanNormal University,2010,(03):741.
[12]邱涛,何诣然*.二次投影算法的扰动分析[J].四川师范大学学报(自然科学版),2012,(01):8.
 QIU Tao,HE Yi ran.Perturbation Analysis of a Double Projection Algorithm[J].Journal of SichuanNormal University,2012,(03):8.

备注/Memo

备注/Memo:
收稿日期:2018-07-04 接受日期:2018-08-24 基金项目:四川省科技厅应用基础项目(2018JY0201) *通信作者简介:何诣然(1973-),男,教授,博导,主要从事最优化理论的研究,E-mail:yiranhe@hotmail.com
更新日期/Last Update: 2020-05-05