求解一类Minimax分式优化问题的几何规划方法

摘要：

研究了一类Minimax分式规划问题(MFP).首先通过引进变量,将问题(MFP)等价转化为问题(EP1),其次,再将问题(EP1)中的约束函数整理成正项式的形式,然后,利用特殊不等式的性质将问题(EP1)转化为易于求解的几何规划问题(GP),通过求解一系列(GP)问题获得原问题的最优解,最后,给出求解问题(MFP)的迭代算法以及算法的收敛性分析,数值结果表明了算法的有效性.

This paper studies a class of Minimax fractional programming problems.Firstly,by introducing variables,the problem(MFP)is equivalently converted to problem(EP1).Secondly,the constraint function in the problem(EP1)is organized into a positive term.Then,by using the properties of special inequalities,problem(EP1)is transformed into an easy-to-solve geometric programming problem(GP),and the optimal solution of the original problem is obtained by solving a series of(GP)problems.Finally,the iterative algorithm for solving problem(MFP)and the convergence analysis of the algorithm are given,and the numerical results show that the algorithm is feasible and effective.

作者：

申培萍 王亚飞 吴殿晓

Shen Peiping;Wang Yafei;Wu Dianxiao(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：

华北水利水电大学数学与统计学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2023年第2期56-62,共7页

Journal of Henan Normal University(Natural Science Edition)

基金：

国家自然科学基金(12071133,11871196).

关键词：

Minimax分式规划 几何规划 迭代算法

Minimax fractional programming geometric programming iterative algorithm

分类号：

O221.2 [理学—运筹学与控制论]

求解一类Minimax分式优化问题的几何规划方法.pdf