求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.

A Deterministic Global Optimization Algorithm for Sum of Linear Ratios Problem

In this paper,a branch and bound algorithm is proposed for globally solving the sum of linear ratios problem.By using an equivalent problem,and a new linear relaxation technique,the initial nonconvex programming problem is reduced to a sequence of linear programming problems.The proposed algorithm convergents to the global optimal solution by means of the subsequent solutions of the series of linear programming problems.The main computation in the algorithm is to solve the sequence of linear programming problems for which standard algorithm are available.Numerical results are given to show the feasibility of the proposed algorithm.