一类新的非线性比式和问题的分枝定界算法(英文)  

A Branch and Bound Algorithm for Solving a New Sum of Nonlinear Ratios Problem

作　　者：李晓爱[1] 刘金伟[2] 

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 [2]新乡学院数学系,河南新乡453003

出　　处：《应用数学》2012年第4期764-770,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11171094,11171368);the Key Scientific and Technological Project of Henan Province (122102210132)

摘　　要：对一类新的非线性比式和问题(SNR)提出分枝定界算法,该问题的研究还很少.首先,通过两层线性化技术,构造一个松弛线性规划,求解该线性规划问题,得到问题(SNR)最优值的下界.其次,介绍新的下界更新技术,证明所给算法的收敛性.A branch and bound algorithm is presented to solve a sum of nonlinear ratios problem （SNR） that there has been little progress on research. First, a linear relaxation programming prob- lem which is solved and provides a lower bound for the optimal value of （SNR） is constructed by a two-level linear relaxation technique. Next, a new updating lower bound technique is introduced. The proposed algorithm is proven to be convergent to a global minimum. The numerical experiments show the feasibility and effectiveness of the algorithm.

关 键 词：全局优化 非线性比式和 分枝定界 更新下界技术 

分 类 号：O221.2[理学—运筹学与控制论]