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运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 159-168.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.012

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无须可微性条件的伪-E-凸函数和伪-E-凸规划的最优性

黄应全1,2,†, 江旭雨3, 宋桂花3, 杨涵3   

  1. 1. 重庆工商大学数学与统计学院, 重庆 400067;
    2. 统计智能计算与监测重庆市重点实验室, 重庆 400067;
    3. 重庆交通大学数学与统计学院, 重庆 400074
  • 收稿日期:2025-08-23 发布日期:2026-06-12
  • 通讯作者: 黄应全 E-mail:huangyq1110@ctbu.edu.cn
  • 基金资助:
    重庆市自然科学基金面上项目 (Nos. cstc2021jcyj-msxmX0499, CSTB2024NSCQ-MSX0973)

Pseudo-E-convex functions without differentiability condition and optimality of pseudo-E-convex programming

HUANG Yingquan1,2,†, JIANG Xuyu3, SONG Guihua3, YANG Han3   

  1. 1 School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
    2 Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing 400067, China;
    3 School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
  • Received:2025-08-23 Published:2026-06-12

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摘要： 本文首先定义了无须可微性条件的伪-E-凸函数,它是E-凸函数和无须可微性条件的伪凸函数的真推广,举例验证了它的存在性,并讨论了它和其他函数的关系,这说明无须可微性条件的伪-E-凸函数更具一般性,应用范围更广;其次,获得了伪-E-凸函数的一些性质；最后,在最优性方面,针对伪-E-凸规划问题($\mathrm{P}$)和($\mathrm{P}_{E}$),讨论了映射E的不动点和它们的全局最优解的关系,得到了规划问题($\mathrm{P}$)的最优解的局部-全局性和全局最优解的唯一性,并分别举例验证了所得结果。

关键词: (严格)伪-E-凸函数, 伪-E-凸规划, 最优解

Abstract: Firstly, a class of pseudo-E-convex functions without differentiability condition is defined in this paper, which is a proper generalization of E-convex functions and pseudoconvex functions without differentiability condition. The existence of such functions is verified with an example. Furthermore, the relationships between pseudo-E- convex functions and other functions are discussed. These indicate that pseudo-E-convex functions without differentiability condition are more general and have a wider range of applications. Secondly, some properties of pseudo-E-convex functions are obtained. Finally, in terms of optimality, the relationship between the fixed points of the mapping E and their global optimal solutions is discussed for the pseudo-E-convex programming problems ($\mathrm{P}$) and ($\mathrm{P}_{E}$), the local-global property of the optimal solutions and the uniqueness of the global optimal solution for programming problem ($\mathrm{P}$) are obtained, and the examples are provided to verify the results respectively.

Key words: (strictly) pseudo-E-convex functions, pseudo-E-convex programming, optimal solutions

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