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线性空间中集值映射向量最优化的最优性条件 被引量:2

Optimality Conditions for Vector Optimization of Set-valued Maps
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摘要 李泽民建立了实线性空间中次似凸集值映射向量最优化问题的K T条件和Lagrange乘子定理。笔者首先引进了广义次似凸集值映射的概念。然后 ,在实线性空间中建立了一个广义次似凸集值映射的择一性定理。最后 ,利用择一性定理 。 Kuhn Tucker optimality conditions and Lagrange multipliers for vector optimization problems with subconvexlike set valued maps wereestablished by Li zemin. Firstly, the concept of generalized subconvexlikeness for set valued maps is introduced in this paper. Then, a theorem of the alternative for generalized subconvexlike set valued maps in real linear spaces is established. Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
出处 《重庆大学学报(自然科学版)》 EI CAS CSCD 北大核心 2003年第3期32-34,88,共4页 Journal of Chongqing University
关键词 集值映射 最优性条件 择一性定理 广义次似凸 实线性空间 set valued maps optimality conditions alternative theorems generalized subconvexlike real linear spaces
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参考文献1

  • 1胡毓达 孟志青.分析与非光滑分析[M].上海:上海科技文献出版社,2000..

同被引文献12

  • 1Li Z M.A Theorem of the Alternative and Its Application to The Optimization of Set-Valued Maps [J].Journal of optimization Theory and Application, 1999, 100 (2): 365-375.
  • 2Huang Y W.A Farkas-Minkowsld Type Altemative Theorem and Its Applications to Set-Valued Equiliborium Problems[J].Journal of Nonlinear and Convex Analysis, 2002,3(1):17-24.
  • 3Li Z M.The Optimality Conditions for Vector Optimization of Set-Valued Maps[J].Journal of Matherntical Analysis and Applications,1999,27(3):413-424.
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  • 7Gong X H.Connectedness of super efficient solution sets for set-valued maps in Banach spaces[J].Mathematical Methods of Operations Research,1996,44:135-146.
  • 8Hu Y D,Ling C.Connectedness of cone super efficient point sets in locally convex topological vector spaces[J].J Optimization Theory and Applications,2000,107(2):433-446.
  • 9Bhatia D,Mehra A.Lagrangian duality for preinvex set-valued functions[J].Journal of Mathematical Analysis and Applications,1997,214:599-612.
  • 10Yang X M,Li D,Wang S Y.Near-subconvexlikeness in vector optimization with set-valued functions[J].J Optimization Theory and Applications,2001,110(2):413-427.

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