方向导数和广义锥-预不变凸集值优化问题

余国林

数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 875-880.

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数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 875-880. DOI: 10.12386/A2011sxxb0088
论文

方向导数和广义锥-预不变凸集值优化问题

    余国林
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Directional Derivatives and Generalized Cone-Preinvex Set-Valued Optimization

    Guo Lin YU
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摘要

讨论拓扑向量空间中无约束集值优化问题的最优性条件问题. 利用集值映射的Dini方向导数, 在广义锥-预不变凸性条件下, 建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件.  

Abstract

This note deals with the optimality conditions of set-valued unconstraint optimization problems in topological vector spaces. Based upon the concepts of Dini directional derivatives and generalized cone-preinvexity for the set-valued mappings, the necessary and sufficient optimality conditions are established for weak and strong minimizer respectively in set-valued optimization problems.  

关键词

集值优化 / 方向导数 / 广义锥-预不变凸集值映射 / 最优性条件

Key words

set-valued optimization / directional derivative / generalized cone-preinvex set-valued mapping

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余国林. 方向导数和广义锥-预不变凸集值优化问题. 数学学报, 2011, 54(5): 875-880 https://doi.org/10.12386/A2011sxxb0088
Guo Lin YU. Directional Derivatives and Generalized Cone-Preinvex Set-Valued Optimization. Acta Mathematica Sinica, Chinese Series, 2011, 54(5): 875-880 https://doi.org/10.12386/A2011sxxb0088

参考文献

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基金

国家自然科学基金资助项目(10901004); 北方民族大学自主科研基金项目(2011)

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