集值映射的超次梯度及其应用

J4 ›› 2012, Vol. 47 ›› Issue (12): 10-13.

集值映射的超次梯度及其应用

徐义红,张小荣,汪涛,段五朵

南昌大学数学系, 江西南昌 330031

收稿日期:2011-12-29 出版日期:2012-12-20 发布日期:2012-12-14
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(2009GZS0021);江西省教育厅科技项目(GJJ12010)

Super subgradient for setvalued map and its applications

XU Yi-hong, ZHANG Xiao-rong, WANG Tao, DUAN Wu-duo

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

Received:2011-12-29 Online:2012-12-20 Published:2012-12-14

摘要/Abstract

摘要：

引进了集值映射的非导数型超次梯度概念,在某种条件下证明了该梯度的存在性。作为应用,在近似锥次类凸假设下,给出了用该次梯度刻画集值优化问题取得超有效元的充分必要条件。

关键词: 超次梯度;超有效元;集值映射

Abstract:

A type of nonderivative super subgradient was introduced for a set-valued map.Under some condition, its existence theorem was proved. As an application, under the assumption of near-subconvexlikeness, the sufficient and necessary optimality conditions were established for set-valued optimization problem to obtain super efficient elements.

Key words: super subgradient; super efficient element; set-valued map

徐义红,张小荣,汪涛,段五朵. 集值映射的超次梯度及其应用[J]. J4, 2012, 47(12): 10-13.

XU Yi-hong, ZHANG Xiao-rong, WANG Tao, DUAN Wu-duo. Super subgradient for setvalued map and its applications[J]. J4, 2012, 47(12): 10-13.

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