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...

Hilbert空间中变分不等式的一种新算法

DOI: 10.3969/j.issn.1001-8395.2015.06.006, PP. 824-829

Keywords: 变分不等式,不动点,非扩张映射,连续映射,单调映射,强收敛

Full-Text   Cite this paper   Add to My Lib

Abstract:

提出在Hilbert空间中求解变分不等式问题的新的混合超梯度算法,在f是单调且连续的映射的假设下,证明由新的混合超梯度算法所生成迭代序列强收敛到变分不等式问题的解集与可数无限个非扩张映射的不动点集合的公共元素.

References

[1]  Facchinei F, Pang J S. Finite-Dimensional Variational Inequalities and Complementary Problems[M]. New York:Springer-Verlag,2003.
[2]  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,2011,217:9543-9511.
[3]  Fang C J, He Y R. An extragradient method for generalized variational inequality[J]. Pacific J Optimization,2013,9:47-59.
[4]  Fang C J, Chen S L. A subgradient extragradient algorithm for solving multi-valued variational inequality[J]. Appl Math Comput,2014,229:123-130.
[5]  Fang C J, Chen S L. A projection algorithm for set-valued variational inequalities on Hadamard manifolds[J]. Optimization Letters,2015,9:779-794.
[6]  Iiduka H, Takahashi W. Strong convergence theorems for nonexpansive nonself-mappings and inverse-strongly-monotone mappings[J]. J Convex Analysis,2004,11(1):69-79.
[7]  Nadezhkina N, Takahashi W. Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings[J]. SIAM J Optimization,2006,16(4):1230-1241.
[8]  Thuy N T T. A new hybrid method for variational inequality and fixed point problems[J]. Vietnam J Mathematics,2013,41(3):353-366.
[9]  Korpelevich G M. The extragradient method for finding saddle points and other problems[J]. Matecon,1976,12:747-756.
[10]  Solodov M V, Svaiter B F. A new projection method for variational inequality problems[J]. SIAM J Control and Optimization,1999,37(3):765-776.
[11]  Takahashi W, Toyoda M. Weak convergence theorems for nonexpansive mappings and monotone mappings[J]. J Optimization Theory and Applications,2003,118(2):417-428.
[12]  Wang X, Li S, Kou X. An extension of subgradient method for variational inequality problems in Hilbert space[J]. Abstract and Applied Analysis,2013:2013.
[13]  Zarantonello E H. Projections on Convex Sets in Hilbert Space and Spectral Theory:Contributions to Nonlinear Functional Analysis[M]. New York:Academic Press,1971.
[14]  Rockafellar R T. On the maximality of sums of nonlinear monotone operators[J]. Transactions of the American Mathematical Society,1970,149:75-88.
[15]  He S, Guo J. Iterative algorithm for common fixed points of infinite family of nonexpansive mappings in Banach spaces[J]. J Appl Math,2012:2012.
[16]  Goebel K, Kirk W A. Topics in Metric Fixed Point Theory[M]. Cambridge:Cambridge University Press,1990.
[17]  Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings[J]. Bulletin of the American Mathematical Society,1967,73(4):591-597.
[18]  Bruck Jr R E. Properties of fixed point sets of nonexpansive mappings in Banach spaces[J]. Transactions of the American Mathematical Society,1973,179:251-262.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133