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集值映射最优化问题的真有效解 被引量：3

Proper Efficiency in Vector Set-Valued Optimization Problem
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摘要 利用Jahn与Rauh提出的集值映射的切上导数概念 。 In this paper, the necessary and sufficient conditions of various proper efficient solutions in vector set-valued optimization problem are obtained by using the concept of contingent epiderivative,which has been introduced by Jahn and Rauh.
作者 刘伟 蔡前凤
机构地区 广东工业大学应用数学系
出处 《广东工业大学学报》 CAS 2001年第2期108-112,共5页 Journal of Guangdong University of Technology
关键词 向量 集值映射 最优化 切上导数 真有效解 vector set-valued otimization contingent epiderivative proper efficiency
分类号 O189 [理学—基础数学] O224 [理学—运筹学与控制论]
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参考文献6

  • 1[1]Aubin J P. Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions[A]. Mathematical Analysis and Applications[C]. Part A, New York: Academic Press, 1981,160-229.
  • 2[2]Aubin J, Ekeland I. Applied Nonlinear Analysis[M]. New York: Wiley, 1984.
  • 3[3]Corley H W. Optimality Conditions for Maximizations of Set-Valued Functions[J]. Journal of Optimization Theory and Applications,1988,58:1-10.
  • 4[4]Luc D T. Contingent Derivatives of Set-Valued Maps and Applications to Vector Optimization[J].Mathematical Programming,1991,50:99-111.
  • 5[5]Jahn J, Rauh R. Contingent Epiderivatives and Set-Valued Optimization[J]. Mathematical Methods of Operations Research, 1997,46: 193-211.
  • 6[6]Gong X H. Connectedness of efficient solution sets for set-valued maps in normed spaces[J]. Journal of Optimization Theory and Applications, 1994,83: 83-96.

同被引文献15

  • 1Yang XQ. Vector Variational Inequality and Vector Pseudolinear Optimization[ J] .Journal d Optimization Theory and Applications, 1997,95(3) :729 - 734.
  • 2Jahn J, Rauh R. Contingent Epiderivatives and Set-Valued Optimization[J].Mathematical Methods of Operations Research,1997,46:193-211.
  • 3Sawaragi Y, Nakayama H,Tanino T. Theory of Multiobjefc Jahn J.and Rauh R.Contingent Epiderivatives and Set-Valued Optimization[J].Mathematical Methods of Operations Research,1997,46:193-211.
  • 4Borwein J M,zhuang D.Super Efficiency in Vector Optimization[J].Transactions of the American Mathematical Society,1993,338(1):105-122.
  • 5Gong XH.Connectedness of Efficient Solution Sets for Set-Valued Maps in Normed Spaces[J].Journal of Optimization Theory and Applications,1994,(83):83-96.
  • 6Jahn J,Rauh R.Contingent Epiderivatives and Set-Valued Optimization[J].Mathematical Methods of Operations Research,1997,46:193-211.
  • 7Corley H W.Optimality Conditions for Maximizations of Set-Valued Functions[J].Journal of Optimization Theory and Applications,1988,58:1-10.
  • 8Aubin J P.Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions[A].Mathematical Analysis and Applications[C].Part A,New York:Academic Press,1981,160-229.
  • 9Luc D T.Contingent Derivatives of Set-Valued Maps and Applications to Vector Optimization[J].Mathematical Programming,1991,50:99-111.
  • 10J. Jahn,A. A. Khan,P. Zeilinger. Second-Order Optimality Conditions in Set Optimization[J] 2005,Journal of Optimization Theory and Applications(2):331～347

引证文献3

二级引证文献2

广东工业大学学报
2001年 第2期

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