求二次比式和问题全局解的一个新的确定性算法  

A New Deterministic Algorithm for Solving the Global Solution of the Generalized Quadratic Ratio Problem

作　　者：张博 高岳林 ZHANG Bo;GAO Yuelin(School of Mathematics and Information Science, North Minzu University, Yinchuan750021, China;Ningxia Scienti c Computing and Intelligent Information Processing Co-innovation Center, Yinchuan 750021, China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]宁夏科学计算与智能信息处理协同创新中心,宁夏银川750021

出　　处：《应用数学》2019年第4期767-777,共11页Mathematica Applicata

基　　金：国家自然科学基金项目(61561001,11161001);宁夏高等教育一流学科建设基金(NXYLXK2017B09);北方民族大学研究生创新项目(YCX18084)

摘　　要：本文研究一类二次比式和规划问题.首先,利用等价转换的方法把原问题转化为一个非线性规划问题,并且这个非线性规划问题的目标函数通项的分子和分母都分别是两项线性函数乘积和再加上一个线性函数的形式,再根据两项线性函数乘积和的特性,对目标函数进行线性松弛,以确定原问题最优值的下界,从而提出一个求解线性规划问题的分支定界算法,并证明该算法的收敛性.最后,数值结果表明所提出的算法是可行有效的.The purpose of this paper is to solve a class of sum-of-quadratic-ratios problem. Firstly , we transform the Original problem into a nonlinear programming problem, in which the form of the molecular and denominator of the ob jective function are composed of the sum of the product of the two linear functions and adding a linear function. Then, according to the characteristic of the programming problem of the product of two linear functions, the ob jective function is loosened linearly to determine the lower bound of the optimal value of the original problem. A branch and bound algorithm for solving linear programming problems is proposed and the convergence of the algorithm is proved. Finally , the numerical results show that the proposed algorithm is feasible and e ective.

关 键 词：全局最优化 分式规划 二次函数 线性乘积和规划 分支定界 线性规划 

分 类 号：O221.2[理学—运筹学与控制论]