期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

二次比式和问题的全局优化方法 被引量：3

Global Optimization Algorithm for Sum of Quadratic Ratios Problem
下载PDF
导出
摘要 利用分枝定界算法,首先将问题(P1)转化为其等价问题(P2),然后利用线性化技术,建立了(P2)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(P2)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 globally solving sum of quadratic ratios problem （P1） , based on the rectanglar partition . Firstly,the problem （P1） is converted into an equivalent problem （P2）. Then, utilizing the linerizing method, a relaxation liner programming probiem （RLP） about （P2） is established. 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. Finally, the numerical experiments show the feasibility of the algorithm.
作者 李晓爱 郑凯 申培萍
机构地区 河南师范大学数学与信息科学学院
出处 《河南师范大学学报（自然科学版）》 CAS CSCD 北大核心 2009年第4期9-11,14,共4页 Journal of Henan Normal University(Natural Science Edition)
基金 国家自然科学基金(10671057)
关键词 二次比式和 分枝定界 线性松弛 sum of quadratic ratios branch and bound liner ralaxation
分类号 O221.2 [理学—运筹学与控制论]
  • 相关文献

参考文献6

  • 1焦红伟,薛臻,申培萍.一类线性比式和问题的全局优化算法[J].河南师范大学学报（自然科学版）,2007,35(1):16-18. 被引量：3
  • 2Freund R W,Jarre F. Sloving the sum-of-ratios problem by an interior-point method[J]. Journal of Global Optimization, 2001,19:83-102.
  • 3Wang Y J,Shen P P,Liang Z. A branch-and-bound algorithm to globally solve the sum of several linear ratios[J]. Applied mathematics and computation, 2005,168:89- 101.
  • 4Qu S J,Zhang K C. An efficient algorithm for globally minimizing sum of quadratic ratios problem with nonconvex quadrtic constraints [J]. Applied mathematics and computation, 2007,189 : 1624-1636.
  • 5Shen P P,Li X A. Accelerating method of global optimization for signomial geometric programming[J]. Journal of Computation and Applied Mathematics, 2008,214 : 66- 77.
  • 6AnL T H,Tao P T. A branch and bound method via d. c. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems[J]. Journal of Global Optimization, 1998,13 : 171-206.

二级参考文献5

  • 1Benson H P.On the global optimization of sums of linear fractional functions over a convex set[J].Journal of Optimization Theory and Applications,2004,121:19-39.
  • 2Konno H,Fukaisi K.A branch and bound algorithm for solving low rank linear multiplicative and fractional programming problems[J].Journal of Global Optimization,2000,18:283-299.
  • 3Wang Y J,Shen P P,Liang Z A.A branch-and-bound algorithm to globally solve the sum of several linear ratios[J].Applied Mathematics and Computation,2005,168:89-101.
  • 4Hoai-Phung,Ng T,Tuy H.A unified monotonic approach to generalized linear fractional programming[J].Journal of Global Optimization,2003,26:229-259.
  • 5Wang Y J,Zhang K C.Global optimization of nonlinear sum of ratios Problem[J].Applied Mathematics and Computation,2004,158:319-330.

共引文献2

同被引文献18

  • 1申培萍,焦红伟.一类非线性比式和问题的全局优化算法[J].河南师范大学学报（自然科学版）,2006,34(3):5-8. 被引量：3
  • 2申培萍.全局优化方法[M].北京:科学出版社,2007.
  • 3袁亚湘,孙文瑜.最优化理论与方法[M].上海:科学出版社,2003:241-384.
  • 4BENSON H P.On the global optimization of sums of linear fractional functions over a convex set[J].Journal of Optimization Theory and Applications,2004,121(1):19-39.
  • 5BENSON H P.Global optimization algorithm for the nunlinear sum of ratios problem[J].Journal of Optimization Theory and Applications,2002,112(1):1-29.
  • 6BENSON H P.Using concave envelopes to globally solve the nonlinear sum of ratios problem[J].Journal of Gobal Optimization,2002,22(1/2/3/4):343-364.
  • 7WANG Yan-jun,ZHANG Ke-cun.Global optimization of nonlinear sum of ratios problem[J].Applied Mathematics and Computation,2004,158(2):319-330.
  • 8BENSON H P. Using concave envelopes to globally solve the nonlinear sum of ratios problem [ J ]. Journal of Global Optimization, 2002, 22:343-364.
  • 9BENSON H P. Global optimization algorithm for the nonlinear sum of ratios problem [ J ]. Journal of Optimi- zation Theory and Applications, 2002, 112 : 1-29.
  • 10SHEN P P, LI X A, JIAO H W. Accelerating method of global optimization for signomial geometric program- ming[J]. Journal of Computational and Applied Math- ematics, 2008,214:66-77.

引证文献3

二级引证文献2

河南师范大学学报（自然科学版）
2009年 第4期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部