一类多乘积和规划问题的矩形分支定界缩减算法  

Rectangular branch and bound reduction algorithm for solving a kind of multi-product-sum programming problems

作　　者：马小华[1] 盛文强 高岳林[1] 

机构地区：[1]北方民族大学信息与系统科学研究所,宁夏银川750021

出　　处：《兰州理工大学学报》2013年第6期137-142,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11161001)

摘　　要：研究一类多乘积和规划问题,根据所研究问题的特殊结构,利用对数函数和指数函数的单调性和凹凸性,给出一个二级线性松弛凸规划问题,以确定全局最优值的下界,使用超矩形缩减技术以提高算法的定界能力,提出一种新的分支定界缩减算法,证明算法的收敛性,数值算例表明所提出的算法是可行的.A kind of multi-product-sum programming problems was studied in this paper.According to the special structure of the problems,using the monotonicity and concavity or convexity of the logarithm and exponential functions,a two-level linear relaxation convex programming problem was given so as to determine the global optimum＇s lower bound.The reduction technology of super-rectangle was used in order to improve the capacity of bounding.Thus,a new branch and bound reduction algorithm was given.The convergence of the algorithm was proved.The numerical examples show that the proposed algorithm was feasible.

关 键 词：全局优化 多乘积和规划 分支定界 超矩形缩减 

分 类 号：O211.1[理学—概率论与数理统计]