共查询到19条相似文献,搜索用时 62 毫秒
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集值映射最优化问题超有效解集的连通性 总被引:7,自引:0,他引:7
本文在局部凸空间中对集值映射最优化问题引入超有效解的概念.首先研究了超 有效点的一些重要特性.其后证明了当目标函数为锥类凸的集值映射时,其目标空间里 的超有效点集是连通的;若目标函数为锥凸的集值映射时,其超有效解集也是连通的. 相似文献
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集值映射最优化问题的严有效解集的连通性及应用 总被引:7,自引:0,他引:7
仇秋生 《高校应用数学学报(A辑)》1999,14(1):11
本文对集值映射最优化问题引入严有效解的概念.证明了当目标函数为锥类凸的集值映射时,其目标空间里的严有效点集是连通的;若目标函数为锥凸的集值映射时,其严有效解集也是连通的.作为应用,讨论了超有效解集的连通性. 相似文献
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集值映射最优化的问题的严有效解集的连通性及应用 总被引:4,自引:0,他引:4
仇秋生 《高校应用数学学报(A辑)》1999,(1):85-92
本文对集值映射最优化问题引入严有效解的概念,证明了当目标函数为锥类凸的集值映射时,其目标空间的严有效点集是连通的; 相似文献
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锥上半连续锥拟凸集值映射多目标优化超有效解集的连通性 总被引:1,自引:0,他引:1
本文研究集值映射多目标优化超有效解集的连通性,在目标映射为锥上半连续和锥拟凸的条件下,证明了其超有效解集是连通的. 相似文献
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锥拟凸集值映射多目标优化的解集的连通性 总被引:1,自引:0,他引:1
在一般拓扑向量空间中,本文引进了一类锥进凸(锥严格拟凸)集值映射。并在目标映射是锥拟凸(锥严格拟凸)和上半连续的条件下,利用Minkowski泛函,证明了弱有效解(有效解)集是连通的。文[9]中的结论是本文所得结果大目标映射为单值和拓扑空间为格的情况下的特例。 相似文献
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Various difficulties have been encountered in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, Benson recently developed a finite, outer-approximation algorithm for generating the set of all efficient extreme points in the outcome set, rather than in the decision set, of problem (MOLP). In this article, we show that the Benson algorithm also generates the set of all weakly efficient points in the outcome set of problem (MOLP). As a result, the usefulness of the algorithm as a decision aid in multiple objective linear programming is further enhanced. 相似文献
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Approximation Methods in Multiobjective Programming 总被引:3,自引:0,他引:3
Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers more than 50 articles published since 1975.His work was supported by Deutsche Forschungsgemeinschaft, Grant HA 1795/7-2.Her work was done while on a sabbatical leave at the University of Kaiserslautern with support of Deutsche Forschungsgemeinschaft, Grant Ka 477/24-1. 相似文献
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序扰动多目标规划的锥次微分稳定性 总被引:9,自引:1,他引:8
对于局部凸拓扑向量空间的多目标规划问题,本文研究并得到当确定空间序的控制锥受扰动,它们的锥有效点(解)集和锥弱有效点(解)集分别在锥次微分和锥弱次微分意义下的稳定性结果. 相似文献
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本文研究了一类由平面上点的表示系统所生成的内部非空的自相似集,证明其边界曲线的一半是三个A-完备集的并集,并给出计算这类完备集的结构矩阵的简单方法,从而利用Marion定理得出这类自相似集边界的Hausdorff维数。 相似文献
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Shuxiang Yu 《Annals of Differential Equations》2011,(4):505-508
In this paper,using the notion of an isolating block and Conley's attractor theory,an existence criterion of trajectories connecting a pair of invariant sets of ordinary differential equations is given. 相似文献
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对满足强分离条件的自相似集,本文给出一种估计填充测度下界的方法,称为部分估计原理。利用这种估计方法得出的某些自相似集的填充测度的下界,往往和准确的填充测度值相等 相似文献
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We consider the numerical solution of the free boundary Bernoulli problem by employing level set formulations. Using a perturbation technique, we derive a second order method that leads to a fast iteration solver. The iteration procedure is adapted in order to work in the case of topology changes. Various numerical experiments confirm the efficiency of the derived numerical method. 相似文献
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D. J. White 《Journal of Optimization Theory and Applications》1995,87(3):727-746
The prime concern in this paper is the interface between efficient solutions and rational reaction sets in multilevel programming. It is shown that there need be no rational reaction solution which is also efficient, although in the bilevel case such a solution always exists, and in the generalK-level case such a solution exists if certain conditions hold. Some theoretical properties of an extension of known methods for generating efficient solutions are given, which are important algorithmically.This work was carried out under the auspices of the University of Manchester, Manchester, England and the University of Virginia, Charlottesville, Virginia, USA. The author thanks the referees for their helpful comments on the original version. 相似文献
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In this paper, we investigate the contractibility of the efficient frontier in a vector maximization problem defined by a continuous vector-valued strictly quasiconcave function
and a convex compact set D in
p
. It is shown that the efficient frontier is contractible if one of the components of g is strongly quasiconcave on X. This work extends a result by Sun (see Ref. 1), which confirms the connectedness of the efficient frontier. 相似文献