一类不确定凸多项式优化的SOS松弛对偶问题

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (2): 285-0292.

一类不确定凸多项式优化的SOS松弛对偶问题

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:2023-09-06 出版日期:2024-03-26 发布日期:2024-03-26
通讯作者: 孙祥凯 E-mail:sunxk@ctbu.edu.cn

SOS Relaxation Dual Problem for a Class of Uncertain Convex Polynomial Optimization

HUANG Jiayi, SUN Xiangkai

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

Received:2023-09-06 Online:2024-03-26 Published:2024-03-26

摘要/Abstract

摘要： 考虑一类目标函数和约束函数均具有谱面不确定数据的平方和(SOS)凸多项式优化问题. 首先, 借助SOS条件建立带有不确定数据的SOS凸多项式系统的择一性定理; 其次, 引入该SOS多项式优化问题的SOS松弛对偶问题, 并刻画它们之间的鲁棒弱对偶性与强对偶性质; 最后, 借助数值算例说明该SOS松弛对偶问题可以重构为半定规划问题.

关键词: SOS凸多项式, 鲁棒对偶性, 择一性定理

Abstract: We considered a class of sum of squares (SOS) convex polynomial optimization problems with spectrahedral uncertainty data in both objective and constraint functions. Firstly, an alternative theorem for SOS-convex polynomial system with uncertain data was established in terms of SOS conditions. Secondly, we introduced a SOS relaxation dual problem for this SOS polynomial optimization problem and characterized the robust weak and strong duality properties between them. Finally, a numerical example was used to demonstrate that the SOS relaxation dual problem could be reformulated as a semidefinite programming problem.

Key words: SOS-convex polynomial, robust duality, alternative theorem

中图分类号:

O221.6

黄嘉译, 孙祥凯. 一类不确定凸多项式优化的SOS松弛对偶问题[J]. 吉林大学学报(理学版), 2024, 62(2): 285-0292.

HUANG Jiayi, SUN Xiangkai. SOS Relaxation Dual Problem for a Class of Uncertain Convex Polynomial Optimization[J]. Journal of Jilin University Science Edition, 2024, 62(2): 285-0292.