删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

无单调性集值变分不等式的一种投影算法

本站小编 Free考研考试/2021-12-27

陈园
四川师范大学数学科学学院, 成都 610068
收稿日期:2018-11-01出版日期:2020-11-15发布日期:2020-11-15


基金资助:国家自然科学基金(11271274)资助.


A PROJECTION ALGORITHM FOR SOLVING MULTI-VALUED VARIATIONAL INEQUALITIES WITHOUT MONOTONICITY

Chen Yuan
Department of Mathematics, Sichuan Normal University, Chengdu 610068, China
Received:2018-11-01Online:2020-11-15Published:2020-11-15







摘要



编辑推荐
-->


本文给出了求解无单调性集值变分不等式的一个新的投影算法,该算法所产生的迭代序列在Minty变分不等式解集非空且映射满足一定的连续性条件下收敛到解.对比文献[10]中的算法,本文中的算法使用了不同的线性搜索和半空间,在计算本文所引的两个数值例子时,该算法比文献[10]中的算法所需迭代步更少.
MR(2010)主题分类:
90C33
90C25
74C05

分享此文:


()

[1] Ferris M C, PANG J S. Engineering and economic applications of complementarity problem[J]. SIAM Rev, 1997, 39:669-713.

[2] Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications[M]. New York:Academic Press, 1980.

[3] Hartman P, Stampacchia G. On some non-linear elliptic differential-functional equations[J]. Acta Mech, 1966, 115:271-310.

[4] Monteiro R D C, Svaiter B F. An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods[J]. SIAM J Optimiz, 2013, 23(2):1092-1125.

[5] Solodov M V, Svaiter B F. A new projection method for variational inequality problems[J]. SIAM J Control Optim, 1999, 37(3):765-776.

[6] 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.

[7] Wang Y J, Xiu N H, Wang C Y. Unified framework of extragradient-type methods for pseudomonotone variational inequalities[J]. J Optimiz Theory App, 2001, 111(3):641-656.

[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] Burachik R S, Millán R D. A projection algorithm for non-monotone variational inequlities. 2016, arXiv:1609.09569.

[11] Ye M L, He Y R. A double projection method for solving variational inequalities without monotonicity. Comput Optim Appl, 2015, 60:141-150.

[12] Facchinei F, Pang J S. Finite-dimensional variational inequalities and complementarity problems[M]. New York:Springer-Verlag, 2003.

[13] Gafni E M, Betsekas D P. Two-metric projection methods for constrained optimization[J]. SIAM J Control Optim, 1984, 22(6):936-964.

[14] Burachik R S, Iusem A N. Set-valued mappings and enlargements of monotone operators[M]. Berlin:Springer, 2008.

[15] Sun D F. A class of iterative methods for solving nonlinear projection equations[M]. Plenum Press, 1996.

[16] Sun D F. A projection and contraction method for the nonlinear complementarity problem and its extensions[J]. Mathematic Numerica Sinica, 1994, 16:183-194.

[17] He Y R. A new double projection algorithm for variational inequalities[J]. J Comput Appl Math, 2006, 183(1):166-173.

[1]尹江华, 简金宝, 江羡珍. 凸约束非光滑方程组一个新的谱梯度投影算法[J]. 计算数学, 2020, 42(4): 457-471.
[2]刘金魁. 解凸约束非线性单调方程组的无导数谱PRP投影算法[J]. 计算数学, 2016, 38(2): 113-124.
[3]李姣芬, 张晓宁, 彭振, 彭靖静. 基于交替投影算法求解单变量线性约束矩阵方程问题[J]. 计算数学, 2014, 36(2): 143-162.
[4]简金宝, 唐菲, 黎健玲, 唐春明. 无约束极大极小问题的广义梯度投影算法[J]. 计算数学, 2013, 35(4): 385-392.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=1907
相关话题/数学 计算 文献 微信 科学学院