均匀凸优化问题的最优性条件和 Lagrange 全对偶

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1255-1267.

均匀凸优化问题的最优性条件和 Lagrange 全对偶

陈泓烨(),方东辉^*(),吴柯幸()

吉首大学数学与统计学院湖南吉首 416000

收稿日期:2024-12-17 修回日期:2025-02-18 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: 2788045301@qq.com
作者简介:E-mail: dh_fang@jsu.edu.cn;|3263014170@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)

Optimality Conditions and Total Lagrange Dualities for Evenly Convex Optimization Problems

Chen Hongye(),Fang Donghui^*(),Wu Kexing()

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

Received:2024-12-17 Revised:2025-02-18 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12261037);Hunan Provincial National Natural Science Foundation of China(2024JJ7396)

摘要/Abstract

摘要：

利用 $c$-次微分概念, 引入新的约束规范条件, 等价刻画了目标函数和约束函数均为真均匀凸函数的约束优化问题的最优性条件以及该问题与其 Lagrange 对偶问题之间的全对偶和稳定全对偶.

关键词: 均匀凸优化问题, Lagrange 对偶, 最优性条件, 全对偶

Abstract:

In this paper, we study an evenly convex optimization problem with the objective function and constraint functions being proper evenly convex. By using the concept of c-subdifferential, we introduce some new notions of constraint qualifications. Under those new constraint qualifications, we provide necessary and sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for the evenly convex optimization problem to have total Lagrangian dualities and stable total Lagrangian dualities.

Key words: evenly convex optimization problem, Lagrange duality, optimality condition, total duality

中图分类号:

O221.2

陈泓烨, 方东辉, 吴柯幸. 均匀凸优化问题的最优性条件和 Lagrange 全对偶[J]. 数学物理学报, 2025, 45(4): 1255-1267.

Chen Hongye, Fang Donghui, Wu Kexing. Optimality Conditions and Total Lagrange Dualities for Evenly Convex Optimization Problems[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1255-1267.

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