拟凸规划近似解的特征刻画和近似对偶理论

数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 640-652.

• • 上一篇

拟凸规划近似解的特征刻画和近似对偶理论

方东辉^*(),王俊颖()

吉首大学数学与统计学院湖南吉首 416000

收稿日期:2024-07-10 修回日期:2024-10-05 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 方东辉 E-mail:dh_fang@jsu.edu.cn;1070938151@qq.com
作者简介:王俊颖，E-mail: 1070938151@qq.com
基金资助:
国家自然科学基金(12261037);湖南省自然科学基金(2024JJ7396)

Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming

Donghui Fang^*(),Junying Wang()

College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2024-07-10 Revised:2024-10-05 Online:2025-04-26 Published:2025-04-09
Contact: Donghui Fang E-mail:dh_fang@jsu.edu.cn;1070938151@qq.com
Supported by:
NSFC(12261037);NSF of Hunan Province(2024JJ7396)

摘要/Abstract

摘要：

利用函数的近似次微分性质和拟凸函数的生成集的概念, 引入一类新的约束规范条件, 建立了拟凸规划问题拟 $(\alpha,\varepsilon )$ -最优解的特征刻画, 近似鞍点定理及混合型对偶理论.

关键词: 拟凸规划, 拟 $(\alpha,\varepsilon )$ -最优解, 近似鞍点定理, 混合型对偶

Abstract:

By using the properties of the approximate subdifferentials of involved functions and generators of quasiconvex functions, we introduce a new constraint qualification. Under this constraint qualification, characterizations of the quasi $(\alpha,\varepsilon)$ -optimal solution, the approximate saddle point theorems and the approximate mixed type duality theorems for quasiconvex programming are established.

Key words: quasiconvex programming, quasi $(\alpha,\varepsilon)$ -optimal solution, approximate saddle point theorem, mixed type duality

中图分类号:

O224

方东辉,王俊颖. 拟凸规划近似解的特征刻画和近似对偶理论[J]. 数学物理学报, 2025, 45(2): 640-652.

Donghui Fang,Junying Wang. Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming[J]. Acta mathematica scientia,Series A, 2025, 45(2): 640-652.

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拟凸规划近似解的特征刻画和近似对偶理论

Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming

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