集值优化Benson真有效元的二阶刻画

doi:10.15960/j.cnki.issn.1007-6093.2016.02.008

运筹学学报

集值优化Benson真有效元的二阶刻画

徐义红^1,* 杨赟¹

1. 南昌大学数学系, 南昌 330031

收稿日期:2014-12-05 出版日期:2016-06-15 发布日期:2016-06-15
通讯作者: 徐义红 xuyihong@ncu.edu.cn
基金资助:
国家自然科学基金(No. 11461044), 江西省自然科学基金(No. 20151BAB201027), 江西省教育厅科技项目(No. GJJ12010)

Second-order characterizations on Benson proper efficient element of set-valued optimization

XU Yihong^1,*YANG Yun¹

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

Received:2014-12-05 Online:2016-06-15 Published:2016-06-15

摘要/Abstract

摘要：

引进了一种新的二阶组合切锥, 利用它引进了一种新的二阶组合切导数, 称为二阶组合径向切导数, 并讨论了它的性质及它与二阶组合切导数的关系, 借助二阶径向组合切导数, 分别建立了集值优化取得Benson真有效元的最优性充分和必要条件.

关键词: 二阶组合径向切导数, 集值优化, Benson真有效元

Abstract:

This paper introduced a new kind of second-order tangent cone, and related second-order tangent derivative, termed as second-order radial composed tangent derivative. Some properties of second-order radial composed tangent derivative and its relationship to second-order composed tangent derivative are discussed. Sufficient and necessary optimality conditions are established respectively for a Benson proper efficient element of set-valued optimization by second-order radial tangent derivative.

Key words: second-order radial composed tangent derivative, set-valued optimization, Benson proper efficient element

徐义红, 杨赟. 集值优化Benson真有效元的二阶刻画[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.02.008.

XU Yihong, YANG Yun. Second-order characterizations on Benson proper efficient element of set-valued optimization[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.02.008.

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集值优化Benson真有效元的二阶刻画

Second-order characterizations on Benson proper efficient element of set-valued optimization

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