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广义变分不等式的广义间隙函数和误差界 被引量：4

Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities
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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. Some classes of generalized gap functions for two kinds of generalized variational inequality problems are considered. Error bounds for the underlying variational inequalities by using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution were obtained. It is not necessary to suppcsethat Fis continuously differential nor of local Lipschitz. with respect to the solution were obtained. It is not necessary to suppose that Fis continuously differentiable local Lipschitz.
作者 胡艳红 宋文
机构地区 东北师范大学数学系 哈尔滨师范大学数学系
出处 《应用数学和力学》 EI CSCD 北大核心 2009年第3期301-308,共8页 Applied Mathematics and Mechanics
基金 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)
关键词 变分不等式 间隙函数 误差界 variational inequality gap functions error bounds
分类号 O221.2 [理学—运筹学与控制论] O29 [理学—应用数学]
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参考文献8

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  • 2Wu J H, Florian M,Marcotte P.A general descent framework for the monotone variational inequality problem[J].Mathematical Programming, 1993,61 (3) : 281-300.
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  • 6Solodov M V. Merit functions and error bounds for generalized variational inequalities[ J]. Journal of Mathematical Analysis and Applications, 2003,287 (2) : 405-414.
  • 7Noor M A. Merit functions for general variational inequalities[ J]. Journal of Mathematical Analysis and Applications, 2006,316(2) : 736-752.
  • 8Qu 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.

同被引文献16

  • 1董宁,莫浩艺,高兴宝.解广义变分不等式的神经网络[J].工程数学学报,2004,21(F12):78-82. 被引量：1
  • 2李有梅,申建中,徐宗本.投影型神经网络算法的全局收敛性分析[J].计算机学报,2005,28(7):1178-1184. 被引量：4
  • 3Noor M A.Merit functions for general variational inequalities[J].J Math Anal Appl,2006,316:736-752.
  • 4Hartman P,Stampacchia G.On some nonlinear elliptic differential functional equations[J].Acta Math,1966,115(1):271-310.
  • 5Gao X B.A novel neural network for nonlinear convex programming[J].IEEE Trans on Neural Networks,2004,15(3):613-621.
  • 6Lan H Y,Cui Y S.A neural network method for solving a system of linear variational inequalities[J].Chaos,Solitons and Fractals,2009,41:1245-1252.
  • 7Ding K,Huang N J.A new class of interval projection neural networks for solving interval quadratic program[J].Chaos,Solitons and Fractals,2008,35:718-725.
  • 8Xia Y S,Feng G.A new neural network for solving nonlinear projection equations[J].Neural Networks,2007,20:577-589.
  • 9Gupta, R. ; Mehra, A. : Gap functions and error bounds for quasi variational inequalities [ J ]. Global Optim,2012, ( 4 ) : 737-748.
  • 10Noor M A. :Merit functions for general variational inequalities [ J ]. Journal of Mathematical Anaysis and Applications, 2006, (2) :736-752.

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应用数学和力学
2009年 第3期

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