一类鲁棒凸优化的Mond-Weir型逼近对偶性

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (3): 539-543.

一类鲁棒凸优化的Mond-Weir型逼近对偶性

赵丹¹, 孙祥凯²

1. 郑州升达经贸管理学院应用数学研究所, 郑州 451191; 2. 重庆工商大学数学与统计学院, 重庆 400067

收稿日期:2018-07-16 出版日期:2019-05-26 发布日期:2019-05-20
通讯作者: 赵丹 E-mail:zd__1008@126.com

MondWeir Type Approximate Duality for a Class of Robust Convex Optimization

ZHAO Dan¹, SUN Xiangkai²

1. Institute of Applied Mathematics, Zhengzhou Shengda University ofEconomics, Business & Management, Zhengzhou 451191, China;2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received:2018-07-16 Online:2019-05-26 Published:2019-05-20
Contact: ZHAO Dan E-mail:zd__1008@126.com

摘要/Abstract

摘要： 通过引入一类含有不确定信息的凸约束优化问题, 先借助鲁棒优化方法, 建立该不确定凸约束优化问题的MondWeir型鲁棒逼近对偶问题, 再借助一类广义鲁棒逼近KKT条件, 刻画该不确定凸约束优化问题与其MondWeir型鲁棒逼近对偶问题之间的逼近对偶性关系.

关键词: 不确定优化问题, 逼近对偶性, 鲁棒KKT条件

Abstract: By introducing a class of convex constrained optimization problems with uncertain data, we first established a MondWeir type robust approximate dual problem for the uncertain convex constrained optimization problem by means of robust optimization method. Then, by means of a class of generalized robusttype approximate KKT conditions, we characterized approximate duality relationship between the uncertain convex constrained optimization problem and its Mond\|Weir type robust approximate dual problem.

Key words: uncertain optimization problem, approximate duality, robust KKT condition

中图分类号:

O221.6

赵丹, 孙祥凯. 一类鲁棒凸优化的Mond-Weir型逼近对偶性[J]. 吉林大学学报(理学版), 2019, 57(3): 539-543.

ZHAO Dan, SUN Xiangkai. MondWeir Type Approximate Duality for a Class of Robust Convex Optimization[J]. Journal of Jilin University Science Edition, 2019, 57(3): 539-543.