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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (4): 1-5.doi: 10.6040/j.issn.1671-9352.0.2016.469

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广义向量变分不等式的间隙函数与误差界

陈霞,陈纯荣*   

  1. 重庆大学数学与统计学院, 重庆 401331
  • 收稿日期:2016-10-10 出版日期:2017-04-20 发布日期:2017-04-11
  • 通讯作者: 陈纯荣(1981— ),男,博士,副教授,研究方向为向量优化研究. E-mail:chencr1981@163.com E-mail:cquchenxia@163.com
  • 作者简介:陈霞(1992— ),女,硕士研究生,研究方向为事向量优化研究. E-mail:cquchenxia@163.com
  • 基金资助:
    国家自然科学基金资助项目(11301567)

Gap functions and error bounds for generalized vector variational inequalities

CHEN Xia, CHEN Chun-rong*   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2016-10-10 Online:2017-04-20 Published:2017-04-11

摘要: 利用线性标量化方法构造广义向量变分不等式的间隙函数,并利用广义f-投影算子的性质验证了正则间隙函数。在广义强伪单调的条件下得到了误差界结论。

关键词: 间隙函数, 广义向量变分不等式, 误差界, 广义强伪单调性, 广义f-投影算子

Abstract: Gap functions for generalized vector variational inequalities were established via linear scalarization approaches. By using some properties of generalized f-projection operators, the regularized gap function was verified. With the condition of the generalized strong pseudomonotonicity, error bounds were obtained.

Key words: gap function, error bound, generalized vector variational inequalities, generalized strong pseudomonotonicity, generalized f-projection

中图分类号: 

  • O221
[1] LI X, LI X S, HUANG N J. A generalized f-projection algorithm for inverse mixed variational inequalities[J]. Optimization Letters, 2014, 8(3):1063-1076.
[2] SUN X K, CHAI Y. Gap functions and error bounds for generalized vector variational inequalities[J]. Optimization Letters, 2014, 8(5):1663-1673.
[3] ZUO X, WEI H Z, CHEN C R. Continuity results and error bounds on pseudomonotone vector variational inequalities via scalarization[J]. Journal of Function Spaces, 2016(3):1-11.
[4] CHARITHA C, DUTTA J. Regularized gap functions and error bounds for vector variational inequalities[J]. Pacific Journal of Optimization, 2010, 6(3):497-510.
[5] SOLODOV M V. Merit functions and error bounds for generalized variational inequalities[J]. Journal of Mathematical Analysis and Applications, 2003, 287(2):405-414.
[6] LI C Q, LI J. Merit functions and error bounds for constrained mixed set-valued variational inequalities via generalized f-projection operators[J]. Optimization, 2016, 65(8):1569-1584.
[7] LI X B, ZHOU L W, HUANG N J. Gap functions and global error bounds for generalized mixed variational inequalities on hadamard mainifolds[J]. Journal of Optimization Theory and Applications, 2016, 168(3):830-849.
[8] NOOR M A. Merit functions for general variational inequalities[J]. Journal of Mathematical Analysis and Applications, 2006, 316(2):736-752.
[9] LEE G M, KIM D S, LEE B S, et al. Vector variational inequality as a tool for studying vector optimization problems[J]. Nonlinear Analysis, 1998, 34:745-765.
[1] 田晓欢,陈纯荣. Ky Fan拟不等式的间隙函数和误差界[J]. 山东大学学报(理学版), 2016, 51(11): 123-126.
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