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向量变分不等式与广义变分不等式之间的某些关系 被引量：3

Certain Relations Between Vector Variational Inequalities and Generalized Variational Inequalities
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摘要 文章首先建立了向量变分不等式与广义变分不等式之间的等价关系,然后利用这个结论,建立了向量变分不等式的Levitin-Polyak适定性与广义变分不等式的Levitin- Polyak适定性之间的等价关系. In this paper, we first establish an equivalence between a vector variational inequality problem and a generalized variational inequality problem. Then we apply this result to establish equivalences among several types of Levitin-Polyak well-posedness of a vector variational inequality problem and a generalized variational inequality problem.
作者 江波 张杰 黄学祥
机构地区 复旦大学管理学院 重庆邮电大学应用数学研究所
出处 《运筹学学报》 CSCD 北大核心 2008年第1期115-120,共6页 Operations Research Transactions
基金 国家自然科学基金 上海市浦江人才计划资助
关键词 运筹学 向量变分不等式 广义变分不等式 近似序列 Levitin—Polyak适定性 Operations research, vector variational inequality, generalized variational inequality, approximating solution sequence, Levitin-Polyak well-posedness
分类号 O178 [理学—基础数学] O177.91 [理学—基础数学]
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参考文献10

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同被引文献20

  • 1Debreu G.A social existence theorem[J].Proceedings of the National Academy of Sciences,1952,38:886-893.
  • 2Arrow K J,Debreu G.Existence of an equilibrium for a competitive economy[J].Econometrica,1954,22:265-290.
  • 3Pang J S,Fukushima M.Quasi-variational inequality,generalized Nash equilibria,and multi-leader-follower games[J].Computational Management Science,2005,2:21-56.
  • 4Fukushima M.Restricted generalized Nash equilibria and constrolled penalty algorithm[J].Computational Management Science,2008,7:21-22.
  • 5Chen G Y,Huang X X,Yang X Q.Vector Optimization,Set-Valued and Variational Analysis[M].Berlin:Springer,2005.
  • 6Giannessi F.Vector Variational Inequalities and Vector Equilibrium-Mathematic Theories[M].Dordrecht:Kluwer Academic Publishers,2000.
  • 7Huang X X,Yang X Q,Teo K L.Convergence analysis of a class of penalty methods for vector optimization oroblems with cone constraints[J].J Global Optimization,2006,36:637-652.
  • 8Huang X X,Yang X Q.Calmness and exact penalization in vector optimization with cone constraints[J].Computational Optimization and Applications,2006,35:47-67.
  • 9Hobbs B F,Pang J S.Nash-Cournot equilibrium in electric power markets with piecewise linear demand functions and joint constraints[J].Operations Research,2007,50:113-127.
  • 10Jiang B,Zhang J,Huang X X.Levitin-Polyak well-posedness of generalized quasivariational ineq-ualities with functional constraints[J].Nonlinear Analysis:TMA,2009,70:1492-1503.

引证文献3

二级引证文献1

运筹学学报
2008年 第1期

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