文献类型：期刊文献

中文题名：带非凸二次约束的二次比式和问题的全局优化算法(英文)

英文题名：An Efficient Algorithm of Global Optimization for Sum of Quadratic Ratios Problem with Nonconvex Quadratic Constraints

作者：李晓爱[1];顾敏娜[2];申培萍[1]

第一作者：李晓爱

机构：[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

第一机构：河南师范大学数学与信息科学学院,河南新乡453007

年份：2010

期号：2

起止页码：438-444

中文期刊名：应用数学

外文期刊名：Mathematica Applicata

收录：CSTPCD;;北大核心:【北大核心2008】；CSCD:【CSCD2011_2012】；

基金：Supported by the National Natural Science Foundation of China(10671057)

语种：中文

中文关键词：全局优化;二次比式和;分枝定界;线性松弛

外文关键词：Sum of quadratic ratios; Global optimization; Linear relaxation; Branch and bound

摘要：对带非凸二次约束的二次比式和问题(P)给出分枝定界算法,首先将问题(P)转化为其等价问题(Q),然后利用线性化技术,建立了(Q)松弛线性规划问题(RLP),通过对(RLP)可行域的细分及求解一系列线性规划问题,不断更新(Q)的上下界,从理论上证明了算法的收敛性,数值实验表明了算法的可行性和有效性.
In this paper a branch and bound approach is proposed for solving sum of quadratic ratios problem with nonconvex quadratic constraints （P）,based on the rectangular partition.Firstly,the problem （P） is converted into an equivalent sum of linear ratios problem with quadratic constrains （Q）.Then,utilizing the linear relaxation technique,a liner relaxation programming problem （RLP） about （Q） is established which is solved and provides a lower bound of the optimal value.The proposed algorithm is convergent to the global minimum through the successive refinement of the feasible region and the solution of a series of the linear programming problems.The numerical experiments show the effectiveness and feasibility of the algorithm.