一类带多项式约束的不确定凸优化问题的鲁棒可行性半径刻画

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1551-1559.

一类带多项式约束的不确定凸优化问题的鲁棒可行性半径刻画

肖彩云(),孙祥凯*()

^{重庆工商大学, 经济社会应用统计重庆市重点实验室, 数学与统计学院重庆 400067}

收稿日期:2021-11-26 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 孙祥凯 E-mail:xcyuncq@163.com;sunxk@ctbu.edu.cn
作者简介:肖彩云, E-mail: xcyuncq@163.com
基金资助:
国家自然科学基金(12001070);重庆市自然科学基金(cstc2020jcyj-msxmX0016);重庆市教委科技项目重点项目(KJZD-K202100803);重庆工商大学研究生创新型科研项目(yjscxx2022-203-185);重庆市巴渝学者青年学者项目

Characterization of the Radius of the Robust Feasibility for a Class of Uncertain Convex Optimization Problems with Polynomial Constraints

Caiyun Xiao(),Xiangkai Sun*()

^{Chongqing Key Laboratory of Social Economy and Applied Statistics, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067}

Received:2021-11-26 Online:2022-10-26 Published:2022-09-30
Contact: Xiangkai Sun E-mail:xcyuncq@163.com;sunxk@ctbu.edu.cn
Supported by:
the NSFC(12001070);the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0016);the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100803);the Innovation Project of CTBU(yjscxx2022-203-185);the Education Committee Project Foundation of Chongqing for Bayu Young Scholar

摘要/Abstract

摘要：

该文旨在刻画一类约束函数是带有不确定信息的凸多项式的不确定凸优化问题的鲁棒可行性半径的下界. 首先借助鲁棒优化方法, 引入了该不确定凸优化问题的鲁棒对等问题(Robust counterpart), 并给出了其鲁棒可行性半径的定义.随后通过引入一类上图集和借助由不确定集所生成的Minkowski泛函, 刻画了该不确定凸优化问题的鲁棒可行性半径的下界.进一步的, 在不确定集是仿射不确定集以及约束函数是平方和凸多项式时, 得到了该不确定优化问题的鲁棒可行性半径的一个精确公式, 推广和改进了文献[10] 的相应结果.

关键词: 多项式约束, 鲁棒可行性, Minkowski泛函

Abstract:

This paper deals with the lower bound of the radius of the robust feasibility for a class of convex optimization problems with uncertain convex polynomial constraints. Following the idea due to robust optimization, we first introduce the robust counterpart of the uncertain convex optimization problem and give the concept of radius of robust feasibility. By using the so-called epigraphical set and the Minkowski functions generated by the uncertain sets, we obtain the lower bound for the radius of robust feasibility of the uncertain convex optimization. Furthermore, an exact formula for the radius of the robust feasibility for an uncertain optimization problem with SOS-convex polynomial constraints is obtained. Our results extend and improve the corresponding results obtained in [10].

Key words: Polynomial constraints, Robust feasibility, Minkowski functions

中图分类号:

O221.8

肖彩云,孙祥凯. 一类带多项式约束的不确定凸优化问题的鲁棒可行性半径刻画[J]. 数学物理学报, 2022, 42(5): 1551-1559.

Caiyun Xiao,Xiangkai Sun. Characterization of the Radius of the Robust Feasibility for a Class of Uncertain Convex Optimization Problems with Polynomial Constraints[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1551-1559.

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