[1]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):299-304.[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,(03):299-304.[doi:10.3969/j.issn.1001-8395.2018.03.003]
点击复制

随机变分不等式的随机投影梯度算法()
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03期
页码:
299-304
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Stochastic Projection Gradient Algorithm for Stochastic Variational Inequalities
文章编号:
1001-8395(2018)03-0299-06
作者:
杨 灿 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 Can XIA Fuquan
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
随机变分不等式 投影算法 伪单调映射 全局收敛性
Keywords:
variational inequality projection algorithm pseudo-monotone mapping globally convergence
分类号:
O176; O178
DOI:
10.3969/j.issn.1001-8395.2018.03.003
文献标志码:
A
摘要:
在Rn空间中给出随机变分不等式问题的随机投影梯度算法.该算法的优点在于:在迭代的每一步,只需向可行集投影一次,也只需对函数赋值一次; 这使得算法简单快速,特别对于F函数值以及投影难以计算的情况.同时,证明该算法所产生的迭代序列的全局收敛性.
Abstract:
We present a stochastic projection gradient algorithm for stochastic variational inequality problems in Euclidean space.The advantage of this algorithm is that we need only one projection onto the set C and only one value of operator F per iteration, which makes it very attractive, especially for cases when the computations of operator F and projection onto C and projection onto e expensive. We also prove the globally convergence of the iterative sequence.

参考文献/References:

[1] BREZIS H. Opérateurs maximaux monotones:et semi-groupes de contractions dans les espaces de Hilbert[J]. J Acoustical Society America,1989,125(4):2680.
[2] GIANNESSI F, Maugeri A. Variational Inequality and Network Equilibrium Problems[M]. New York:Plenum Press,1995:315-320.
[3] VERMA R U. General convergence analysis for two-step projection methods and application to variational problems[J]. Appl Math Lett,2005,18(11):1286-1292.
[4] FACCHINEI F, PANG J S. Finite-dimensional Variational Inequalities and Complementary Problems Volume I/II[M]. New York:Springer-Verlag,2003.
[5] LUO Z Q, PANG J S, RALPH D. Mathematical Programs with Equilibrium Constraints[M]. Cambridge:Cambridge University Press,1996.
[6] CHEN F Y, YAN H, YAO L. A newsvendor pricing game[J]. IEEE Transactions on Systems Man and Cybernetics Part A Systems and Humans,2004,34(4):450-456.
[7] CMAHAIAN S, VAN RYZIN G. Inventory competition under dynamic consumer choice[J]. Operations Research,2001,49(5):464-657.
[8] BASAR T, OLSDER G. Dynamic Noncooperative Game Theory[M]. Philadeiphia:SIAM,1999.
[9] FILAR J, VRIEZE K. Competitive Markov Decision Processes[M]. Berlin:Springer-Verlag,1996.
[10] GURKAN G, ÖZGE A Y, ROBINSON S M, et al. Sample path solution of stochastic variational inequalities,with applications to option pricing[C]. Proceedings of the 28th conference on Winter simulation-WSC 96,1996. DOI:10.1145/256562.256646.
[11] GURKAN G, OZGE A Y, ROBINSON S M. Sample-path solution of stochastic variational inequalities[J]. Mathematical Programming,1999,84(2):313-333.
[12] ROBINSON S M. Analysis of sample-path optimization[J]. Mathematics of Operations Research,1996,21(3):513-528.
[13] SHAPIRO A, DENTCHEVA D, RUSZCZYNSKI A. Lectures on Stochastic Programming:Modeling and Theory[M]. Philadeiphia:SIAM,2009.
[14] XU H. Sample average approximation methods for a class of stochastic variational inequality problems[J]. Asia Pacific Operational Research,2011,27(1):103-119.
[15] ROBBINS H, MONRO S. A stochastic approximation method[J]. Ann Mathematical Statistics,1951,22(3):400-407.
[16] ROBINSON S M, MONRO S. On a stochastic approximation method[J]. Ann Mathematical Statistics,1954,25(3):463-483.
[17] JIANG H Y, XU H F. Stochastic approximation approaches to the stochastic variational inequality problem[J]. IEEE Transactions on Automatic Control,2008,53(6):1462-1475.
[18] KOSHAL J, NEDIC A, SHANBHAG U V. Regularized iterative stochastic approximation methods for stochastic variational inequality problems[J]. IEEE Transactions on Automatic Control,2013,58(3):594-609.
[19] NEMIROVSKI A, JUDITSKY A, LAN G, et al. Robust stochastic approximation approach to stochastic programming[J]. SIAM J Optim,2009,19(4):1574-1609.
[20] JUDITSKY A, NEMIROVSKI A, TAUVEL C. Solving variational inequalities with stochastic mirror-prox algorithm[J]. Stochastic Systems,2011,1(1):17-58.
[21] BERTSEKAS D P, TSITSIKLIS J M. Neuro-dynamic programming[J]. Athena Scientific,1996,27:1687-1692.
[22] ERMOLIEV Y. Stochastic Quasigradient Methods, Numerical Techniques for Stochastic Optimization[M]. New York:Springer-Verlag,1988.
[23] KUSHNER H J, YIN G. Stochastic Approximation and Recursive Algorithms and Applications[M]. New York:Springer-Verlag,2003.
[24] ORMAN A. Optimization of stochastic models, the interface between simulation and optimization[J]. Operational Research Society,1998,49(6):675-675.
[25] FREY J. Introduction to stochastic search and optimization:estimation,simulation, and control[J]. Wiley-Interscience,2004,46(3):368-369.
[26] MALITSKY Y. Projected reflected gradient methods for monotone variational inequalities[J]. SIAM J Optim,2015,25(1):502-520.
[27] BAIOCCHI C, CAPELO A. Variational and Quasivariational Inequalities[M]. New York:John Wiley,1984.
[28] ROBBINS H, SIEGMUND D. A convergence theorem for nonnegative almost supermartingales and some applications[C]//Optimizing Methods in Statistics. Rustagi J S, ed. New York:Academic,1971:233-257.
[29] PFLUG G C. Optimization of stochastic models[C]//The Interface Between Simulation and Optimization. New York:Kluwer Academic,1996.

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,(03):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,(03):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,(03):265.
[4]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.[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,(03):471.[doi:10.3969/j.issn.1001-8395.2018.04.007]

备注/Memo

备注/Memo:
收稿日期:2017-01-16 接受日期:2017-03-01
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,主要从事最优化理论及应用的研究,E-mail:fuquanxia@163.com
更新日期/Last Update: 2018-03-15