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一类新的二阶组合切导数及其应用

周丽霞1  徐义红1,*  吕强1   

  1. 1. 南昌大学数学系, 南昌 330031
  • 收稿日期:2016-02-01 出版日期:2017-09-15 发布日期:2017-09-15
  • 通讯作者: 徐义红 xuyihong@ncu.edu.cn

A new kind of second-order composed tangent derivatives and its applications

ZHOU Lixia1  XU Yihong1,*   L\"{U} Qiang1   

  1. 1. Department of Mathematics, Nanchang University, Nanchang 330031, China
  • Received:2016-02-01 Online:2017-09-15 Published:2017-09-15
  • Supported by:

    国家自然科学基金 (No. 11461044), 江西省自然科学基金 (No. 20151BAB 201027), 江西省教育厅科技项目 (No. GJJ12010)

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摘要：

引进了一种新的切锥, 讨论它与相依切锥的关系. 借助这种新的切锥引进了一类新的二阶组合切导数, 并讨论了它与其他二阶切导数的关系. 利用这类新的二阶组合切导数, 建立了集值优化分别取得Henig有效元和全局有效元的最优性必要条件.

关键词: 切锥, 二阶组合切导数, Henig 有效元, 全局有效元

Abstract:

A new kind of tangent cones is introduced, whose relationship to the contingent cone is discussed. With the introduced cones, a new kind of second-order tangent derivatives, termed  second-order composed tangent derivatives, is developed, and its relationship to other second-order composed tangent derivatives is discussed. Then, with the help of second-order composed tangent derivatives, optimality necessary conditions are established respectively for a Henig efficient solution and a globally proper efficient solution of set-valued optimization.

Key words: tangent cone, second-order composed tangent derivative, Henig efficient element, globally proper efficient element