一类不确定优化问题的鲁棒对偶性刻画

吉林大学学报(理学版)

一类不确定优化问题的鲁棒对偶性刻画

孙祥凯¹, 曾静¹, 郭晓乐²

1. 重庆工商大学数学与统计学院, 重庆 400067; 2. 西南政法大学经济学院, 重庆 401120

收稿日期:2015-09-28 出版日期:2016-07-26 发布日期:2016-07-20
通讯作者: 孙祥凯 E-mail:sxkcqu@163.com

Characterizations of Robust Duality for a Class ofUncertain Optimization Problems

SUN Xiangkai¹, ZENG Jing¹, GUO Xiaole²

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;[JP]2. School of Economics, Southwest University of Political Science and Law, Chongqing 401120, China

Received:2015-09-28 Online:2016-07-26 Published:2016-07-20
Contact: SUN Xiangkai E-mail:sxkcqu@163.com

摘要/Abstract

摘要：

通过引入一类目标函数和约束条件均带有不确定信息的优化问题, 借助鲁棒型次微分约束品性, 刻画了该不确定优化问题与其不确定对偶问题之间的Mond-Weir型鲁棒对偶性, 即原问题的鲁棒对应与其对偶问题的最优对应之间的对偶性.

关键词: 不确定优化问题, 鲁棒对偶性, 约束品性

Abstract:

By introducing a class of optimization problems with uncertainty information both in the objective functions and constraints, and then using the robusttype subdifferential constraint qualification, we characterized MondWeir type robust duality between the uncertain optimization problem and its uncertain dual problem, in other words, the duality between the robust counterpart of the primal problem and the optimistic counterpart of its dual problem.

Key words: uncertain optimization problem, robust duality, constraint qualification

中图分类号:

O221.6

孙祥凯, 曾静, 郭晓乐. 一类不确定优化问题的鲁棒对偶性刻画[J]. 吉林大学学报(理学版), 2016, 54(04): 715-719.

SUN Xiangkai, ZENG Jing, GUO Xiaole. Characterizations of Robust Duality for a Class ofUncertain Optimization Problems[J]. Journal of Jilin University Science Edition, 2016, 54(04): 715-719.

[1]	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.
[2]	赵丹, 孙祥凯. 复合凸优化问题的稳定强对偶[J]. J4, 2013, 51(03): 441-443.