共查询到16条相似文献,搜索用时 46 毫秒
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没有凸锥的闭性和点性假设,该文考虑由一般凸锥生成的单调Minkowski泛函并研究其性质.由此,在偏序局部凸空间的框架下,通过利用单调连续Minkowski泛函和单调连续半范,该文分别获得了一般集合及锥有界集合的弱有效点的标量化.利用此弱有效性的标量化,该文分别推导出一般集合及锥有界集合的Henig真有效点的标量化.进而,当序锥具备有界基时,该文获得局部凸空间中超有效性的一些标量化结果.最后,该文给出Henig真有效性和超有效性的稠密性结果.这些结果推广并改进了有关的已知结果. 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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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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赋范线性空间集合的严有效点 总被引:25,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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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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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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本文指出《集值优化问题Henig真有效解的最优性条件》一文的主要结论是《近似锥-次类凸集值优化的严有效性》一文相应结论的特例. 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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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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本文研究了Orlicz-Sobolev空间的弱局部一致凸性.通过运用Orlicz空间和Sobolev空间的技巧,得到了赋Luxemburg范数的Orlicz-Sobolev空间具有弱局部一致凸性的充要条件和赋Orlicz范数的Orlicz-Sobolev空间具有弱局部一致凸性的充分条件. 相似文献
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In the context of vector optimization and generalizing cones with bounded bases, we introduce and study quasi-Bishop-Phelps cones in a normed space X. A dual concept is also presented for the dual space X*. Given a convex subset A of a normed space X partially ordered by a closed convex cone S with a base, we show that, if A is weakly compact, then positive proper efficient points are sequentially weak dense in the set E(A, S) of efficient points of A; in particular, the connotation weak dense in the above can be replaced by the connotation norm dense if S is a quasi-Bishop-Phelps cone. Dually, for a convex subset of X* partially ordered by the dual cone S
+, we establish some density results of positive weak* efficient elements of A in E(A, S
+). 相似文献
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We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators. 相似文献