一类非凸约束优化问题的近似最优性条件及其混合型对偶

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 651-660.

一类非凸约束优化问题的近似最优性条件及其混合型对偶

王娇浪(),方东辉*()

^{吉首大学数学与统计学院湖南吉首 416000}

收稿日期:2021-08-12 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 方东辉 E-mail:1334806781@qq.com;dh_fang@jsu.edu.cn
作者简介:王娇浪, E-mail: 1334806781@qq.com
基金资助:
国家自然科学基金(11861033);湖南省自然科学基金(2020JJ4494);吉首大学科研基金(Jdy20069);吉首大学科研基金(JGY202139)

Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems

Jiaolang Wang(),Donghui Fang*()

^{College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000}

Received:2021-08-12 Online:2022-06-26 Published:2022-05-09
Contact: Donghui Fang E-mail:1334806781@qq.com;dh_fang@jsu.edu.cn
Supported by:
the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Jishou University(Jdy20069);the Scientific Research Fund of Jishou University(JGY202139)

摘要/Abstract

摘要：

利用函数Fréchet次微分性质, 引入新的约束规范条件, 建立了目标函数和(或)约束函数为α-凸函数的非凸约束优化问题的近似最优性条件以及该问题及其混合型对偶问题之间的弱对偶、强对偶和逆对偶定理.

关键词: 非凸约束优化问题, 约束规范条件, 近似最优性条件, 混合型对偶

Abstract:

By using the properties of the Fréchet subdifferentials, we first introduce a new constraint qualification and then establish some approximate optimality conditions for the non-convex constrained optimization problem with objective function and/or constraint function being α-convex function. Moreover, some results for the weak duality, strong duality and converse-like duality theorems between this non-convex optimization problem and its mixed type dual problem are also given.

Key words: Non-convex constraint optimization problem, Constraint qualification, Approximate optimality conditions, Mixed type duality

中图分类号:

O224

王娇浪,方东辉. 一类非凸约束优化问题的近似最优性条件及其混合型对偶[J]. 数学物理学报, 2022, 42(3): 651-660.

Jiaolang Wang,Donghui Fang. Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems[J]. Acta mathematica scientia,Series A, 2022, 42(3): 651-660.

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