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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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集值映射多目标规划问题的解集的连通性 总被引:6,自引:2,他引:4
傅万涛 《高校应用数学学报(A辑)》1994,(3):321-328
本文研究了无限维空间里集值映射的多目标规划问题。主要结果是:当目标函数为类凸的集值映射时,其目标空间里的有效点集是连通的;若目标函数为C-凸的集值映射时,其有效解集也连通。 相似文献
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本文在自反Banach空间中引进了锥弱连续映射和点集的弱连通概念.在讨论锥弱连续和锥拟凸映射以及锥最小上界的几个性质的基础上,证明了当象集为锥凸集时定义在自反Ba- nach空间中的有界闭凸集上的锥弱连续和锥拟凸映射多目标最优化问题的锥有效解集是弱连通的. 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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本文研究赋范线性空间中集值映射向量优化问题超有效解集的连通性问题.证明了目标映射为锥拟凸的向量优化问题的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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利用连通集上有关上半连续点集映射的连通性质,本文证明了拓扑向量空间中向量最优化问题的弱锥-有效解集与相应目标空间中的弱锥-有效点集连通性之间的一个等价定理. 相似文献
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In this paper, we study Henig weakly efficient solutions for set-valued optimization problems. The connectedness of the Henig
weakly efficient solution set is proved under the condition that the objective function be a cone-arcwise connected set-valued
mapping. As an application of the result, we establish the connectedness of the set of super efficient solutions. 相似文献
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The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set, respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems. 相似文献
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研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理. 相似文献
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本文研究拓扑空间中锥拟凸多目标优化问题的有效解集的连通性.在目标映射是上连续和拟凸(次严格拟凸)的条件下,证明了锥弱有效(有效)解集是连通的.进一步,在是连续和强拟凸的条件下,证明了锥有效解集是路连通的. 相似文献
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In this paper, we first derive several characterizations of the nonemptiness and compactness for the solution set of a convex scalar set-valued optimization problem (with or without cone constraints) in which the decision space is finite-dimensional. The characterizations are expressed in terms of the coercivity of some scalar set-valued maps and the well-posedness of the set-valued optimization problem, respectively. Then we investigate characterizations of the nonemptiness and compactness for the weakly efficient solution set of a convex vector set-valued optimization problem (with or without cone constraints) in which the objective space is a normed space ordered by a nontrivial, closed and convex cone with nonempty interior and the decision space is finite-dimensional. We establish that the nonemptiness and compactness for the weakly efficient solution set of a convex vector set-valued optimization problem (with or without cone constraints) can be exactly characterized as those of a family of linearly scalarized convex set-valued optimization problems and the well-posedness of the original problem. 相似文献