运筹学学报(中英文) ›› 2025, Vol. 29 ›› Issue (4): 72-82.doi: 10.15960/j.cnki.issn.1007-6093.2025.04.006

• 论文 • 上一篇    下一篇

弱半E-凸规划问题的最优性条件

王小芳1, 梁治安1,*(), 高彩霞1   

  1. 1. 内蒙古大学数学科学学院, 内蒙古呼和浩特 010021
  • 收稿日期:2022-11-16 出版日期:2025-12-15 发布日期:2025-12-11
  • 通讯作者: 梁治安 E-mail:zhianl@163.com
  • 基金资助:
    国家自然科学基金(12461057)

Optimality conditions of weakly semi-E-convex programming

Xiaofang WANG1, Zhian LIANG1,*(), Caixia GAO1   

  1. 1. School of Mathematics and Science, Inner Mongolia University, Hohhot 010021, Inner Mongolia, China
  • Received:2022-11-16 Online:2025-12-15 Published:2025-12-11
  • Contact: Zhian LIANG E-mail:zhianl@163.com

摘要:

本文引入了一类新的广义凸函数: 弱半$E$-凸函数, 建立了其对应的弱半$E$-凸规划问题; 讨论了弱半$E$-凸规划问题的解的性质, 并给出弱半$E$-凸规划问题的最优性条件。

关键词: 弱半E-凸函数, 弱半E-凸规划问题, 鞍点, 稳定点, 最优性条件

Abstract:

In this paper, we introduce a new class of generalized convex functions: weakly semi-$E$-convex functions and establish its corresponding weakly semi-$E$-convex programming. We discuss the properties of solutions of weakly semi-$E$-convex programming and give the optimality conditions of weakly semi-$E$-convex programming.

Key words: weakly semi-E-convex functions, weakly semi-E-convex programming, saddle points, stable points, optimality conditions

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