一类两阶段自适应鲁棒多目标规划的对偶性刻画

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 185-194.

一类两阶段自适应鲁棒多目标规划的对偶性刻画

黄嘉译(),孙祥凯^*()

重庆工商大学数学与统计学院重庆 400067

收稿日期:2023-02-07 修回日期:2023-10-07 出版日期:2024-02-26 发布日期:2024-01-10
通讯作者: 孙祥凯, E-mail:sxkcqu@163.com
作者简介:黄嘉译, E-mail：huangjyzk@163.com
基金资助:
国家自然科学基金(11701057);重庆市自然科学基金(cstc2021jcyj-msxmX1191);重庆市教委重点项目(KJZD-K202100803);重庆市研究生创新基金项目(CYS23566)

Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming

Huang Jiayi(),Sun Xiangkai()

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2023-02-07 Revised:2023-10-07 Online:2024-02-26 Published:2024-01-10
Supported by:
NSFC(11701057);Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX1191);Key Projects of Chongqing Municipal Education Commission(KJZD-K202100803);Innovation Fund Projects of Chongqing Graduate Student(CYS23566)

摘要/Abstract

摘要：

该文主要研究一类目标函数和约束函数均具有谱面不确定数据的两阶段自适应鲁棒多目标规划问题. 首先, 建立具有仿射自适应变量的两阶段自适应鲁棒多目标规划问题的 Farkas 引理. 随后, 引入该多目标规划问题的半定规划对偶问题. 最后, 借助该 Farkas 引理, 刻画它们之间的对偶性质.

关键词: 自适应鲁棒规划, Farkas引理, 对偶性

Abstract:

In this paper, we deal with a class of two-stage adjustable robust multi-objective programming problems with spectrahedral uncertainty data in both objective and constraints. We first establish a Farkas lemma for a two-stage adjustable robust multiobjective programming with affine adjustable variable. Then, we propose a semidefinite programming dual problem for this multiobjective programming problem. Furthermore, in terms of the obtained Farkas lemma, we explore duality properties between them.

Key words: Adjustable robust programming, Farkas lemma, Duality

中图分类号:

O221.6

黄嘉译, 孙祥凯. 一类两阶段自适应鲁棒多目标规划的对偶性刻画[J]. 数学物理学报, 2024, 44(1): 185-194.

Huang Jiayi, Sun Xiangkai. Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming[J]. Acta mathematica scientia,Series A, 2024, 44(1): 185-194.

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