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集值映射向量优化问题是最优化理论中的一个重要方向.在集值映射为生成锥内部-锥一类凸(简记为ic-锥类凸)的假设条件下,利用择一定理,给出了集值映射向量优化问题ε-弱有效解和ε-有效解的最优性条件和ε-Lagrange乘子定理,是弱有效解和有效解相应结果的推广. 相似文献
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The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior. 相似文献
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余丽 《数学的实践与认识》2012,42(8):207-213
在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的ε-强有效性.在内部锥类凸假设下,利用凸集分离定理,分别建立了关于ε-强有效解的标量化定理和ε-Lagrange乘子定理. 相似文献
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余国林 《应用泛函分析学报》2012,(2):206-212
讨论集值向量优化的标量化和鞍点问题.在生成锥内部凸-锥-类凸假设下,建立了集值向量优化问题在(弱)有效和Benson真有效意义下的标量化定理和鞍点定理. 相似文献
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On super efficiency in set-valued optimization 总被引:1,自引:0,他引:1
The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker's, Lagrange's and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker's, Lagrange's and saddle points optimality conditions are derived. 相似文献
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在实线性空间中引进ic-锥-类凸性和超有效性概念,只利用线性结构而不涉及拓扑结构分别给出实线性空间中超有效解在通常凸性和ic-锥-类凸性条件下的标量化定理。 相似文献
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本文讨论生成锥内部凸-锥-类凸集值向量优化问题的超有效解.在生成锥内部凸-锥类凸假设下,建立了集值向量优化问题在超有效意义下的标量化、Lagrangian乘子和鞍点定理 相似文献
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