集值优化问题ε-强有效元的Lagrange型最优性条件

J4 ›› 2013, Vol. 48 ›› Issue (3): 80-83.

集值优化问题ε-强有效元的Lagrange型最优性条件

徐义红, 韩倩倩,汪涛,吕强

南昌大学数学系, 江西南昌 330031

收稿日期:2012-10-22 出版日期:2013-03-20 发布日期:2013-03-14
作者简介:徐义红(1969- ),男,教授,博士,主要从事多目标规划研究.Email:xuyihong@ncu.edu.cn
基金资助:
国家自然科学基金资助项目(10461007);江西省自然科学基金资助项目(20122BAB201003);江西省教育厅科技项目(GJJ12010)

Lagrange optimality conditions for set-valued optimization problem in the sense of ε-strongly efficient elements

XU Yi-hong, HAN Qian-qian, WANG Tao, L Qiang

Department of Mathematics, Nanchang University, Nanchang 330031, Jiangxi, China

Received:2012-10-22 Online:2013-03-20 Published:2013-03-14

摘要/Abstract

摘要：

利用近似锥-次类凸集值映射的性质证明了当序偶集值映射是近似锥-次类凸时,对应的Lagrange函数也是近似锥-次类凸的。利用此结果得到集值优化问题取得ε强有效元的Lagrange型必要条件,利用ε-强有效元的性质得到Lagrange型充分条件。

关键词: ε-强有效元;近似锥-次类凸;集值优化

Abstract:

By applying properties of the nearly cone-subconvexlike setvalued map, the result was proved that for a nearly cone-subconvexlike ordered pair set-valued map, its relevant Lagrange map is also nearly cone-subconvexlike. With help of such result, a Lagrange optimality necessary condition was established in the sense of ε-strongly efficiency. By taking advantage of properties of an ε-strongly efficient point, a Lagrange optimality sufficient condition was also obtained.

Key words: ε-strongly efficient element; near cone-subconvexlikeness; set-valued optimization

徐义红, 韩倩倩,汪涛,吕强. 集值优化问题ε-强有效元的Lagrange型最优性条件[J]. J4, 2013, 48(3): 80-83.

XU Yi-hong, HAN Qian-qian, WANG Tao, L Qiang. Lagrange optimality conditions for set-valued optimization problem in the sense of ε-strongly efficient elements[J]. J4, 2013, 48(3): 80-83.

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