一类不确定分式多项式优化问题的鲁棒最优解研究  

On Robust Optimal Solutions for a Class of Uncertain Fractional Polynomial Optimization Problems

作　　者：冉波 孙祥凯[1] 郭晓乐 Ran Bo;Sun Xiangkai;Guo Xiaoe(Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring,School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,统计智能计算与监测重庆市重点实验室,重庆400067

出　　处：《数学物理学报(A辑)》2025年第2期630-639,共10页Acta Mathematica Scientia

基　　金：重庆市自然科学基金(CSTB2024NSCQ-MSX0651);重庆市研究生导师团队建设项目(yds223010)。

摘　　要：不确定数据处理过程中常常会涉及到平方和凸凹多项式结构的分式优化问题.该文旨在研究它的鲁棒最优解.首先,借助鲁棒优化方法和一类法锥型约束规格条件,建立该不确定分式多项式优化问题的鲁棒最优解的最优性条件.随后,引入该不确定分式多项式优化问题的鲁棒对偶问题,并研究它们之间的鲁棒弱对偶与强对偶性质.最后,刻画该不确定分式多项式优化问题的精确平方和松弛性质.Fractional optimization with sum of squares convex-concave polynomials is often involved in the uncertain data processing.This paper is concerned with its robust optimal solutions.We first give optimality conditions of robust optimal solutions for the uncertain fractional polynomial optimization problem in terms of robust optimization and a normal cone constraint qualification condition.Then,we give a robust dual problem to this uncertain fractional polynomial optimization problem and establish robust weak and strong duality properties between them.Moreover,we obtain exact sum of squares relaxation results for this uncertain fractional polynomial optimization problem.

关 键 词：分式优化 鲁棒最优性 鲁棒对偶性 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]