[1]杨 博,夏福全*.广义混合变分不等式问题的投影算法[J].四川师范大学学报(自然科学版),2018,(04):471-477.[doi:10.3969/j.issn.1001-8395.2018.04.007]
 YANG Bo,XIA Fuquan.The Projection Algorithm for Solving Generalized Mixed Variational Inequalities[J].Journal of SichuanNormal University,2018,(04):471-477.[doi:10.3969/j.issn.1001-8395.2018.04.007]
点击复制

广义混合变分不等式问题的投影算法()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年04期
页码:
471-477
栏目:
基础理论
出版日期:
2018-04-15

文章信息/Info

Title:
The Projection Algorithm for Solving Generalized Mixed Variational Inequalities
文章编号:
1001-8395(2018)04-0471-07
作者:
杨 博 夏福全*
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
YANG Bo XIA Fuquan
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
广义混合变分不等式 投影算法 Armijo 线搜索 超平面
Keywords:
variational inequalities projection algorithm Armijo linesearch superplane
分类号:
O176; O177
DOI:
10.3969/j.issn.1001-8395.2018.04.007
文献标志码:
A
摘要:
提出一种新的求解广义混合变分不等式的投影算法.在迭代的每一步,首先利用当前点xi,通过计算预解算子得到点zi,其中的迭代步长满足某种Armijo线搜索.然后,利用zi构造出分离当前点xi及广义混合变分不等式解集的超平面,再将当前点向该超平面做投影得到下一步迭代点.在一定的条件下,给出该算法产生的无穷序列具有全局收敛性.同时,给出数值计算结果,表明这种算法的有效性.
Abstract:
This paper presents a new projection algorithm for solving the generalized mixed variational inequalities.At each step of the iteration, the current point xi is first utilized, and the zi is obtained by calculating the resolvent operator, with the iteration step size satisfying with some kind of Armijo linesearch.Then, we use zi to construct a superplane to separate the current point xi to construct a superplane to separate the current point d solution set of generalized mixed variational inequalities.After that, the current point is projected into the superplane to get the next iteration point.Under certain conditions, the infinite sequence generated by the algorithm is globally convergent.At the same time, the numerical results show that the algorithm is effective.

参考文献/References:

[1] SOlODOV M V, SVAITER B F.A new projection method for variational inequality problems[J].SIAM J Control Optim,1999,37(3):765-776.
[2] YUAN X M, LIN M.An lqp-based decomposition for solving a class of variational inequalities[J].SIAM J Optim,2011,21(4):1309-1318.
[3] IUSEM A N, SVAITER B F.A variant of kopelevich's method for variational inequalities with inequalities[J].J Comput Appl Math,1997,42(4):309-321.
[4] HE Y R.A new double projection algorithm for variational inequalities[J].J Comput Appl Math,2006,185(1):166-173.
[5] HASSINA G, DJAMEl B.New effective projection method for variational inequalities problem[J].Rairo-oper Res,2015,49(4):805-820.
[6] ZHENG L.The subgradient double projection method for variational inequlities in a Hilbert space[J].Fixed Point Theory Appl,2013,2013(1):1-14.
[7] ANH P N, LE D M, STROSIOT J J.Generalized projection method for non-lipschitz multivalued monotone variational inequalities[J].Acta Math Vietnam,2009,34(1):67-79.
[8] FANG C J, HE Y R.A new projection algorithm for generalized variational inequality[J].J Inequal Appl,2010,2010(1):1-8.
[9] XIA F Q, HUANG N J.A projection-proximal point algorithm for solving generalized variational inequalities[J].J Optim Theory Appl,2011,150(1):98-117.
[10] FANG C J, CHEN S L.A subgradient algorithm for solving multi-valued variational inequality[J].Appl Math Comput,2014,229(1):123-130.
[11] CHEN H B, WANG Y J, WANG G.Strong convergence of extragradient method for gengeralized variational inequalities in Hilbert space[J].J Inequal Appl,2014,2014(1):1-11.
[12] 陈方琴,夏福全.Hilbert空间中广义变分不等式的近似-似投影算法[J].四川师范大学学报(自然科学版),2012,35(3):297-302.
[13] ANH P N, MUU L D, NGUYEN V H, et al.Using the banach contraction principle to implement the proximal point method for multi-valued monotone variational inequalities[J].J Optim Theory Appl,2005,124(2):285-306.
[14] LI F, HE Y R.An algorithm for generlized variational inequality with pseudomonotone mapping[J].J Comput Appl Math,2009,228(1):212-218.
[15] HE Y R.A new projection algorithm for mixed variational inequalities[J].Acta Math Sci,2007,A27(2):215-220.
[16] TANG G J, ZHU M, LIU H W.A new extragradient-type method for mixed varaitional inequalities[J].Oper Res Lett,2015,43(6):567-572.
[17] TU K, XIA F Q.A projection-type algorithm for solving generalized mixed variational inequalities[J].Acta Math Sci,2016,B36(6):1619-1630.
[18] BREZIS H.Operateurs Maximaux Monotone et Semi-groupes De Contractions Sans Les Espaces De Hilbert[M].Amsterdam:North-Holland Publishing Company,1973.
[19] AUBIN J P, FRANKOWSKA H.Set-Valued Analysis[M].Boston:Birkhause,1990.
[20] AUBIN J P, EKELAND I.Applied Nonlinear Analysis[M].New York:John Wiley and Sons Incorporated,1984.

相似文献/References:

[1]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,(04):741.
[2]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,(04):8.
[3]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,(04):265.
[4]付冬梅,何诣然*.广义混合变分不等式的Tikhonov正则化方法[J].四川师范大学学报(自然科学版),2014,(01):12.
 FU Dongmei,HE Yiran.The Tikhonov Regularization Method for Generalized Mixed Variational Inequalities[J].Journal of SichuanNormal University,2014,(04):12.
[5]杨 灿,夏福全*.随机变分不等式的随机投影梯度算法[J].四川师范大学学报(自然科学版),2018,(03):299.[doi:10.3969/j.issn.1001-8395.2018.03.003]
 YANG Can,XIA Fuquan.Stochastic Projection Gradient Algorithm for Stochastic Variational Inequalities[J].Journal of SichuanNormal University,2018,(04):299.[doi:10.3969/j.issn.1001-8395.2018.03.003]

备注/Memo

备注/Memo:
收稿日期:2016-11-11 接受日期:2017-02-24
基金项目:教育部科学技术重点项目(212147)
*通信作者简介:夏福全(1973—),男,教授,主要从事分拆理论与优化算法设计研究,E-mail:fuquanxia@163.com
更新日期/Last Update: 2018-04-15