集值优化强有效解的广义二阶锥方向导数刻画

运筹学学报 ›› 2013, Vol. 17 ›› Issue (4): 80-86.

集值优化强有效解的广义二阶锥方向导数刻画

徐义红^1,*, 孙鑫¹, 汪涛¹

1. 南昌大学数学系, 南昌 330031；

出版日期:2013-12-15 发布日期:2013-12-15
通讯作者: 徐义红 E-mail:xuyihong@ncu.edu.cn
基金资助:
国家自然科学基金 (No. 61175127), 江西省自然科学基金 (No. 20122BAB201003), 江西省教育厅科技基金 (No. GJJ12010)

Characterizations on strongly efficient solutions of set-valued optimization with generalized second-order cone-directed derivatives

XU Yihong^1,*, SUN Xin¹, WANG Tao¹

1. Department of Mathematics, Nanchang University, Nanchang 330031, China

Online:2013-12-15 Published:2013-12-15

摘要/Abstract

摘要： 在实赋范线性空间中考虑集值优化问题的强有效性. 借助Henig扩张锥和基泛函的性质，利用广义二阶锥方向相依导数，得到受约束于集值映射的优化问题，取得强有效元的二阶最优性必要条件. 当目标函数为近似锥-次类凸映射时, 利用强有效点的标量化定理，得到集值优化问题，取得强有效元的二阶充分条件.

关键词: 强有效性, 广义二阶锥方向相依导数, 集值优化

Abstract: The strong efficiency for set-valued optimization is considered in real normed spaces. With the help of the properties of Henig dilating cone and base functional, by applying generalized second-order cone-directed contingent derivates, a second-order optimality necessary condition is established for a pair to be a strongly efficient element of set-valued optimization whose constraint condition is determined by a set-valued mapping. When objective function is nearly cone-subconvexlike, with the scalarization theorem for a strongly efficient point an optimality sufficient condition is also derived for a pair to be a strongly efficient element of set-valued optimization.

Key words: strong efficiency, generalized second-order cone-directed contingent deriv-ate, set-valued optimization

中图分类号:

O221

徐义红, 孙鑫, 汪涛. 集值优化强有效解的广义二阶锥方向导数刻画[J]. 运筹学学报, 2013, 17(4): 80-86.

XU Yihong, SUN Xin, WANG Tao. Characterizations on strongly efficient solutions of set-valued optimization with generalized second-order cone-directed derivatives[J]. Operations Research Transactions, 2013, 17(4): 80-86.

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