近似锥-次类凸集值优化的严有效性

徐义红;刘三阳

系统科学与数学 ›› 2004, Vol. 24 ›› Issue (3) : 311-317.

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PDF(249 KB)
系统科学与数学 ›› 2004, Vol. 24 ›› Issue (3) : 311-317. DOI: 10.12341/jssms10341
论文

近似锥-次类凸集值优化的严有效性

    徐义红(1),刘三阳(2)
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ON STRICT EFFICIENCY IN SET-VALUED OPTIMIZATION WITH NEARLY CONE-SUBCONVEXLIKENESS

    Yi Hong XU(1),San Yang LIU(2)
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摘要

在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的 严有效性.在近似锥-次类凸假设下, 利用凸集分离定理, 分别得到了Kuhn-Tucker型和Lagrange型最优性条件, 建立了与(VP)等价的两种形式的无约束优化.

Abstract

The set-valued optimization problem with constraints (VP) is considered in the sense of strict efficiency in Hausdorff locally convex linear topological spaces. Under the assumption of the nearly cone- subconvexlikeness, by applying separation theorem for convex sets, Kuhn-Tucker type and Lagrange type optimality conditions for (VP) are derived respectively, and two kinds of unconstrained programs equivalent to (VP) are established.

关键词

严有效性 / 近似锥-次类凸 / 集值优化 / 锥.

Key words

Strict efficiency / nearly cone-subconvexlikeness / set-valued optimization / cone.

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徐义红 , 刘三阳. 近似锥-次类凸集值优化的严有效性. 系统科学与数学, 2004, 24(3): 311-317. https://doi.org/10.12341/jssms10341
Yi Hong XU , San Yang LIU. ON STRICT EFFICIENCY IN SET-VALUED OPTIMIZATION WITH NEARLY CONE-SUBCONVEXLIKENESS. Journal of Systems Science and Mathematical Sciences, 2004, 24(3): 311-317 https://doi.org/10.12341/jssms10341
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