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一类比式和问题的全局优化方法(英文) 被引量：1

Global Optimization for a Class of Sum of Ratios Problems
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摘要 对于一类比式和问题(P)给出一全局优化算法.首先利用线性约束的特征推导出问题(P)的等价问题(P1) ,然后利用新的线性松弛方法建立了问题(P1)的松弛线性规划(RLP) ,通过对目标函数可行域线性松弛的连续细分以及求解一系列线性规划,提出的分枝定界算法收敛到问题(P)的全局最优解.最终数值实验结果表明了该算法的可行性和高效性. A global optimization algorithm is proposed for solving a class of sum of ratios problems （P）. Firstly,an equivalent problem （P1） of the （P） is derived by exploiting the characteristics of linear constraints. Then, by utilizing a new linear relaxation method the relaxation linear program- ming （RLP） of the （P1） can be constructed and the proposed algorithm is convergent to the global minimum of the （P） through the successive refinement of the linear relaxation of feasible region of the objective function and solutions of a series of （RLP）. And finally the numerical experiments are given to illustrate the feasibility and efficiency of the proposed algorithm.
作者 焦红伟 郭运瑞 陈永强
机构地区 河南科技学院数学系 河南师范大学数学与信息科学学院
出处 《应用数学》 CSCD 北大核心 2009年第1期20-26,共7页 Mathematica Applicata
基金 Supported by the National Natural Science Foundation of China(10671057) Natural Science Foundation of Henan Institute of Science and Technology(06054 ,06055)
关键词 比式和 全局优化 线性松弛方法 分枝定界 Sum of ratios Global optimization Linear relaxation method Branch and bound
分类号 O221.2 [理学—运筹学与控制论]
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参考文献9

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同被引文献8

  • 1Konno H,Watanabe H.Bond portfolio optimization problems and their application to index tracking:a partial optimization approach[J].J.Oper.Res.Soc.Jpn.,1996,39:295-306.
  • 2Rao M R.Cluster analysis and mathematical programming[J].J.Am.Stat.Assoc.,1971,66:622-626.
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  • 7Benson H P.Global optimization algorithm for the nonlinear sum of ratios problem[J].JOTA,2002,112(1):1-29.
  • 8Horst R,Pardalos P M,Thoai N V.Introduction to Global Optimization[M].Boston:Kluwer Academic Publishers,2000.

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应用数学
2009年 第1期

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