共查询到15条相似文献,搜索用时 62 毫秒
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利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画. 相似文献
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本文引进了C#-单调范数的概念.利用这个概念,我们给出了Henig有效点的切比雪夫标量化结果. 相似文献
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仇秋生 《高校应用数学学报(A辑)》1999,14(3):329-332
在局部有界的Hausdorff局部凸空间中讨论了集合的真有效点集的连通性问题。证明了当序锥具有基底时,任何非空紧凸集的真有效点集是连通的。 相似文献
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给出实的赋范空间中集值映射的Henig真有效解集的一些性质,并利用集值映射的相依上图导数和集值映射的次微分给出了集值优化问题Henig真有效解的最优性条件的充要条件. 相似文献
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与多目标规划问题的G恰当有效解相应,引进了集合的G恰当有效点的概念,并互研究了G恰当有效点集和G恰当有效解集的连通性.利用所得的结果,还获得多目标规划问题的Pareto有效解集是连通的一个新的结论。 相似文献
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本文推广了Benson真有效点的定义,给出了凸锥相对内部的一个刻划,并在无尖性假设情况下,利用凸锥相对内部的刻划,证明了Hartley真有效点与改进的Benson真有效点是等价的;同时给出了一些有效点与真有效点标量化的一些结果. 相似文献
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Jing Hui QIU 《数学学报(英文版)》2009,25(3):445-454
Applying the theory of locally convex spaces to vector optimization, we investigate the relationship between Henig proper efficient points and generalized Henig proper efficient points. In particular, we obtain a sufficient and necessary condition for generalized Henig proper efficient points to be Henig proper efficient points. From this, we derive several convenient criteria for judging Henig proper efficient points. 相似文献
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赋范线性空间集合的严有效点 总被引:27,自引:2,他引:25
本文引入一个新的有效点概念一严有效点,它是Borwein超有效点的推广.此外还讨论了严有效点的基本性质:存在性条件、纯量化特征、稠密性定理以及与Borwein超有效点的关系. 相似文献
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Scalarization of Henig Proper Efficient Points in a Normed Space 总被引:1,自引:0,他引:1
In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base. 相似文献
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Truong Xuan Duc Ha 《Journal of Mathematical Analysis and Applications》2010,364(1):156-170
In this paper we consider, for the first time, approximate Henig proper minimizers and approximate super minimizers of a set-valued map F with values in a partially ordered vector space and formulate two versions of the Ekeland variational principle for these points involving coderivatives in the sense of Ioffe, Clarke and Mordukhovich. As applications we obtain sufficient conditions for F to have a Henig proper minimizer or a super minimizer under the Palais-Smale type conditions. The techniques are essentially based on the characterizations of Henig proper efficient points and super efficient points by mean of the Henig dilating cones and the Hiriart-Urruty signed distance function. 相似文献
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Existence and density results are established for positive proper efficient points, Henig proper efficient points, and superefficient points in cone compact sets. 相似文献