一类带反凸约束的非线性比式和问题的全局优化算法  

A Global Optimization Algorithm for Sum of Nonlinear Ratios Problem with Reverse Convex Constraints

作　　者：申培萍[1] 王俊华[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《应用数学》2012年第1期126-130,共5页Mathematica Applicata

基　　金：国家自然基金(11171094);河南省科技创新杰出青年基金(09410050001)

摘　　要：本文针对一类带有反凸约束的非线性比式和分式规划问题,提出一种求其全局最优解的单纯形分支和对偶定界算法.该算法利用Lagrange对偶理论将其中关键的定界问题转化为一系列易于求解的线性规划问题.收敛性分析和数值算例均表明提出的算法是可行的.This paper presents a simplicial branch and duality bound algorithm for globally solving a class of the sum of nonlinear ratios fractional programming problems with reverse convex constraints.The algorithm uses Lagrange duality theory to convert the bounding subproblems during the algorithm into a series of linear programming problems,which can be solved very efficiently.The convergence analysis and numerical examples show that the proposed algorithm is feasible.

关 键 词：全局优化 分支定界 反凸约束 非线性比式和 

分 类 号：O221.2[理学—运筹学与控制论]