求二次比式和问题全局解的一个新的确定性算法

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.

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

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.