全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

改进的超梯度算法在无穷维Hilbert空间强收

, PP. 605-609

Keywords: 超梯度算法,Hilbert空间,弱收敛,强收敛,伪单调

Full-Text   Cite this paper   Add to My Lib

Abstract:

许多算法被提出用来解决变分不等式问题,其中最简单的是G.M.Korpelevich(Matecon,1976,12747-756.)超梯度算法.此算法被许多学者所改进.其中文献(Y.J.Wang,N.H.Xiu,J.Z.Zhang.JOptimTheoryAppl,2003,119167-168.)改进的超梯度算法不用假设解存在,并且可以通过迭代产生的点列的收敛性检验解的存在性.将Y.J.Wang,N.H.Xiu和J.Z.Zhang改进的超梯度算法推广到无穷维Hilbert空间,并讨论在无穷维Hilbert空间中改进的超梯度算法的迭代序列关于伪单调变分不等式的解的强收敛性质.

References

[1]  [1] Korpelevich G M. The extragradient method for finding saddle points and other problems[J]. Matecon,1976,12:747-756.
[2]  Khobotov E N. Modification of the extragradient method for solving variational inequalities and certain optimization problems[J]. USSR Computational Mathematics and Mathematical Physics,1987,27:120-127.
[3]  Iusem A N. An iterative algorithm for the variational inequality problem[J]. Computational and Applied Mathematics,1994,13:103-114.
[4]  Marcotte P. Application of Khobotov’s to variational inequalities and network equilibrium problems[J]. Information Systems and Operational Research,1991,29:258-270.
[5]  Sun D. A new stepsize skill for solving a class of nonlinear projection equations[J]. Journal of Computational Mathematics,1995,13:357-368.
[6]  Solodov M V, Tseng P. Modified projection-type methods for monotone variational inequalities[J]. SIAM Journal on Control and Optimization,1996,34:1814-1830.
[7]  Konnov I V. A class of combined iterative method for solving variational inequalities[J]. Journal of Optimization Theory and Applications,1997,35:677-693.
[8]  He B S. A class of projection and contraction methods for monotone variational inequalities[J]. Applied Mathematics and Optimization,1997,35:69-76.
[9]  Iusem A N, Svaiter B F. A variant of Korpelevich’s method for variational inequalities with a new search strategy[J]. Optimization,1997,42:309-321.
[10]  Solodov M V, Svaiter B F. A new projection method for variational inequality problem[J]. SIAM Journal on Control and Optimization,1999,37:765-776.
[11]  Wang Y J, Xiu N H, Zhang J Z. Modified extragradient method for variational inequalities and verification of solution existence[J]. Journal of Optimization Theory and Applications,2003,119:167-168.
[12]  Kinderlehere D, Stampacchia G. An Introduction to Variational Inequalities and Applications[M]. New York:Academic Press,1980.
[13]  Solodov M, Svaiter B F. A new projection method for variational inequality problems[J]. SIAM Journal on Control and Optimization,1999,37:765-776.
[14]  Cottle R W, Pang J S, Stone R E. The Linear Complementarity Problem[M]. New York:Academic Press,1992.
[15]  Li M, Liao L Z, Yuan X M. A modified projection method for co-coercive variational inequality[J]. European Journal of Operational Research,2008,189:310-323.
[16]  Yan X H, Han D R, Sun W Y. A modified projection method with a new direction for solving variational inequalities[J]. Applied Mathematics,2009,211:118-129.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133