带消失约束的区间值优化问题的最优性条件与对偶定理

doi:10.15960/j.cnki.issn.1007-6093.2023.01.006

运筹学学报 ›› 2023, Vol. 27 ›› Issue (1): 87-102.doi: 10.15960/j.cnki.issn.1007-6093.2023.01.006

带消失约束的区间值优化问题的最优性条件与对偶定理

王海军¹^,*(), 王辉辉¹

1. 太原师范学院数学系, 山西晋中 030619

收稿日期:2021-02-07 出版日期:2023-03-15 发布日期:2023-03-16
通讯作者: 王海军 E-mail:wanghjshx@126.com
作者简介:王海军, E-mail: wanghjshx@126.com
基金资助:
山西省高等学校科技创新项目(2019L0784);山西省回国留学人员科研资助项目(2017164);太原师范学院博士科研启动项目

Optimality conditions and duality theorems for interval-valued optimization problems with vanishing constraints

Haijun WANG¹^,*(), Huihui WANG¹

1. Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, Shanxi, China

Received:2021-02-07 Online:2023-03-15 Published:2023-03-16
Contact: Haijun WANG E-mail:wanghjshx@126.com

摘要/Abstract

摘要：

本文考虑一类带消失约束的非光滑区间值优化问题(IOPVC)。在一定的约束条件下得到了问题(IOPVC)的LU最优解的必要和充分性最优性条件, 研究了其与Mond-Weir型对偶模型和Wolfe型对偶模型之间的弱对偶, 强对偶和严格逆对偶定理, 并给出了一些例子来阐述我们的结果。

关键词: 局部Lipschitz函数, 最优性条件, 区间值优化问题, 消失约束, 对偶定理

Abstract:

In this paper, a class of nonsmooth interval-valued optimization problem with vanishing constraints (IOPVC) is considered. The necessary and sufficient optimality conditions for LU optimal solution of (IOPVC) are obtained under some constraint qualifications. The weak duality, strong duality and strict converse duality theorems between (IOPVC) and the corresponding Mond-Weir type and Wolfe type dual models are studied. Furthermore, some examples are given to illustrate our results.

Key words: locally Lipschitz function, optimality conditions, interval-valued optimization problems, vanishing constraints, duality theorems

中图分类号:

O221

王海军, 王辉辉. 带消失约束的区间值优化问题的最优性条件与对偶定理[J]. 运筹学学报, 2023, 27(1): 87-102.

Haijun WANG, Huihui WANG. Optimality conditions and duality theorems for interval-valued optimization problems with vanishing constraints[J]. Operations Research Transactions, 2023, 27(1): 87-102.

参考文献 19

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带消失约束的区间值优化问题的最优性条件与对偶定理

Optimality conditions and duality theorems for interval-valued optimization problems with vanishing constraints

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