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广义变分不等式的广义间隙函数和误差界

胡艳红 宋文

胡艳红, 宋文. 广义变分不等式的广义间隙函数和误差界[J]. 应用数学和力学, 2009, 30(3): 301-308.
引用本文: 胡艳红, 宋文. 广义变分不等式的广义间隙函数和误差界[J]. 应用数学和力学, 2009, 30(3): 301-308.
HU Yan-hong, SONG Wen. Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities[J]. Applied Mathematics and Mechanics, 2009, 30(3): 301-308.
Citation: HU Yan-hong, SONG Wen. Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities[J]. Applied Mathematics and Mechanics, 2009, 30(3): 301-308.

广义变分不等式的广义间隙函数和误差界

基金项目: 国家自然科学基金资助项目(10671050);黑龙江省自然科学基金资助项目(A200607)
详细信息
    作者简介:

    胡艳红(1978- ),女,山东人,讲师,博士生(E-mail:yhhumaths@yahoo.com.cn);宋文,教授(联系人.Tel:+86-451-88060562;E-mail:wsong@hrbnu.edu.cn).

  • 中图分类号: O221.2;O29

Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities

  • 摘要: 针对两类广义变分不等式,分别定义了几族广义间隙函数,并研究其性质.利用这些广义间隙函数,在所研究变分不等式问题的目标函数F关于解是g-强单调的条件下,得到了误差界估计,这里不需要假设F是连续可微或局部Lipschitz的.
  • [1] Fukushima M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems[J].Mathematical Programming,1992,53(1):99-110. doi: 10.1007/BF01585696
    [2] Wu J H,Florian M,Marcotte P.A general descent framework for the monotone variational inequality problem[J].Mathematical Programming,1993,61(3):281-300. doi: 10.1007/BF01582152
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    [4] Huang L R,Ng K F. Equivalent optimization formulations and error bounds for variational inequality problem[J].Journal of Optimization Theory and Applications,2005,125(2):299-314. doi: 10.1007/s10957-004-1839-7
    [5] Tan L L. Regularized gap functions for nonsmooth variational inequality problems[J].Journal of Mathematical Analysis and Applications,2007,334(2):1022-1038. doi: 10.1016/j.jmaa.2007.01.025
    [6] Solodov M V.Merit functions and error bounds for generalized variational inequalities[J].Journal of Mathematical Analysis and Applications,2003,287(2):405-414. doi: 10.1016/S0022-247X(02)00554-1
    [7] Noor M A. Merit functions for general variational inequalities[J].Journal of Mathematical Analysis and Applications,2006,316(2):736-752. doi: 10.1016/j.jmaa.2005.05.011
    [8] Qu B, Wang C Y,Zhang J Z. Convergence and error bound of a method for solving variational inequality problems via the generalized D-gap function[J].Journal of Optimization Theory and Applications,2003,119(3):535-552. doi: 10.1023/B:JOTA.0000006688.13248.04
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  • 被引次数: 0
出版历程
  • 收稿日期:  2008-08-18
  • 修回日期:  2008-12-15
  • 刊出日期:  2009-03-15

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