共查询到19条相似文献,搜索用时 296 毫秒
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集值映射的广义梯度和全局真有效解 总被引:1,自引:1,他引:0
本文利用集值映射的上图导数引进了全局真有效意义下的广义梯度和广义次微分的概念,并且给出了集值映射全局真有效次微分的存在定理,还建立了集值向量优化问题全局真有效解在次微分形式下的最优性条件. 相似文献
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1978年和1979年,Harfley 和 Benson 用不同的方法推广了 G-真有效点的定义。1985年,应玫茜证明了,Hartley 真有效点必为 Benson 真有效点,且在一定条件下Benson 真有效点也为 Hardey 真有效点。本文指出,只要控制锥为闭凸锐(有人称为尖的)的,则 Hartley 的定义等价于 Benson 的定义。 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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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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本文引进集值映射的全局真有效次微分的概念,并用它得到了约束集值优化问题全局真有效解在集值映射的支撑函数和Lagrange乘子形式下的最优性必要条件. 相似文献
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周志昂 《数学的实践与认识》2012,42(1):247-250
在局部凸空间中锥弱似凸集值映射的假设下,集值优化问题Borwein真有效解与Benson真有效解的等价性被获得.为了说明结果,一些例子被给出. 相似文献
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Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space. 相似文献
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Fu Wantao 《数学年刊B辑(英文版)》1994,15(2):173-180
This papeer studies the known density theorem of Arrow-Barankin-Blackwell. The following main result is obtained: If X is a Hausdorff locally convex Topological space and C belong to X is a closed convex cone with bounded base, then for every nonempty weakly compact convex subset A, the set of positive proper efficient points of A is dense in the set of efficient points of A. 相似文献
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FU WANTAO 《数学年刊B辑(英文版)》1994,(2)
ONTHETHEOREMOFARROW-BARANKIN-BLACKWELLFORWEAKIYCOMPACTCONVEXSET¥FUWANTAOAbstract:ThispaperstudiestheknowndensitytheoremofArro... 相似文献
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Strong efficiency in a locally convex space 总被引:12,自引:0,他引:12
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多目标规划的局部较多最优性和局部较多有效性 总被引:3,自引:0,他引:3
多目标规划的局部较多最优性和局部较多有效性胡毓达(上海交通大学应用数学系,200030)国家自然科学基金资助项目.1991年8月27日收到.一、引言考虑多目标规划问题其中XS是约束集(开集(m2)是向量目标函数.对于问题(VMP),自50年代以来人们... 相似文献
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We introduce the concept of positive proper efficient solutions to the generalized system in this paper. We show that, under
some suitable conditions, the set of positive proper efficient solutions is dense in the set of efficient solutions to the
generalized system. We discuss also the connectedness of the set of efficient solutions for the generalized system with monotone
bifunctions in real locally convex Hausdorff topological vector spaces.
This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science
Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC. 相似文献
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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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D. M. Zhuang 《Journal of Optimization Theory and Applications》1991,71(3):613-620
In this note, we establish some interesting relationships between the existence of Borwein's proper efficient points and the existence of bases for convex ordering cones in normed linear spaces. We show that, if the closed unit ball in a smooth normed space ordered by a convex cone possesses a proper efficient point in the sense of Borwein, then the ordering cone is based. In particular, a convex ordering cone in a reflexive space is based if the closed unit ball possesses a proper efficient point. Conversely, we show that, in any ordered normed space, if the ordering cone has a base, then every weakly compact set possesses a proper efficient point.The research was conducted while the author was working on his PhD Degree under the supervision of Professor J. M. Borwein, whose guidance and valuable suggestions are gratefully appreciated. The author would like to thank two anonymous referees for their constructive comments and suggestions. This research was supported by an NSERC grant and a Mount Saint Vincent University Research Grant. 相似文献