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实线性空间中的广义向量类凸性(英文) 被引量：1

The generalized vector convex-like mappings on real linear spaces
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摘要 作者利用向量闭包给出了实线性空间上广义向量类凸映射的一个性质,并依此说明在向量优化问题中,如果约束映射是广义向量类凸的则Slater约束品性成立.另外,作者利用鞍点准则刻画了实线性空间中的真有效性. By using the concept of vector closure, a property of the generalized vector convexlike maps on real linear spaces is presented and it is showed that the Slater constraint qualification for vector optimization holds if the constraint mapping is the generalized vector convexlike. Furthermore, characterization of proper efficiency is established in terms of saddle-point criterion.
作者 余国林 刘三阳
机构地区 西安电子科技大学应用数学系
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第2期229-232,共4页 Journal of Sichuan University(Natural Science Edition)
基金 陕西省自然科学基金项目(2000SL03) 宁夏商算学校科学研究项目(200710)
关键词 广义向量类凸性 向量闭包 Slater约束品性 真有效性 鞍点 generalized vector convexlikeness, vector closure, slater constraint qualification, proper efficiency, saddle point
分类号 O221 [理学—运筹学与控制论]
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参考文献4

  • 1Adan M, Novo V. Proper efficiency in vector optimization on real linear spaces[J]. Journal of Optimization and Application, 2004, 121(3): 515.
  • 2Adan M, Novo V. Weak efficiency in vector optimization using a closure of algebraic type under cone convexlikeness[J]. European Journal of Operational Research, 2003, 149: 641.
  • 3Adan M, Novo V. Optimality conditions for vector optimization problems with generalized convexity in real linear spaces[J]. Optimization, 2002, 51: 73.
  • 4Adan M, Novo V. Partial and generalized subconvexity in vector optimization problem[J]. Journal of Convex Analysis, 2001, 8: 583.

同被引文献11

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  • 7Brando A J,Rojas-Medar M A,Silva G N.Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces[J].J Optim Theory Appl,1999,103(1):65.
  • 8Mishra S K,Giorgi G,Wang S Y.Duality in vector optimization in Banach spaces with generalized convexity[J].J Global Optim,2004,29(2):415.
  • 9Hu Y D,Ling C.The generalized optimality conditions of multi-objective programming problem in topological vector space[J].J Math.Anal Appl,2004,290(1):363.
  • 10Yu G L,Liu S Y.Some vector optimization problems in Banach spaces with generalized convexity[J].Computers and Mathematics with Applications,2007,54(2):1403.

引证文献1

四川大学学报（自然科学版）
2008年 第2期

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