全文下载：2013060643
周雪刚
(广东金融学院 应用数学系，广东 广州 510521)
摘要：提出了一种新的线性乘性规划问题（LMP）的因式输出空间分支定界算法，首先利用目标函数中每个乘积项的一个因式作为变量构成输出空间，并对其进行超矩形的对分，同时在每次迭代时用松弛线性规划确定原问题（LMP)的下界，并证明了算法的收敛性，数值实验表明提出的方法是可行的。
关键词：线性乘性规划； 全局最优化； 输出空间； 分支定界
中图分类号： O 221.2文献标志码： A
A Factors’ Outcome Space Branch and Bound Algorithm for Solving Linear Multiplicative Programming
ZHOU Xue-gang
( Department of Applied Mathematics, Guangdong University of Finance,Guangzhou 510521, China)
Abstract:A new branch and bound algorithm for solving linear multiplicative programming is proposed. Firstly, each of multiplier factors in any product item of objective function is as variable to construct outcome space. The outcome space which is a super-rectangular is partitioned. The proposed algorithm computes the lower bounds by solving linear relaxation programming problems in any iteration. And the convergence of the proposed determinate global optimization algorithm is proved. Numerical experiments are given to illustrate the feasibility of the proposed algorithm.
Key words:linear multiplicative programming; global optimization; outcome space; branch and bound
收稿日期：2013-01-16
基金项目： 广东省自然科学基金博士科研启动基金项目（S2013040012506)；广东金融学院科研项目（2012RCYJ005）.
作者简介： 周雪刚（1974—），男，博士.
