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一类广义非线性比式和问题的全局优化算法 被引量：1

A kind of global optimal algorithm for the sum of generalized nonlinear ratios
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摘要 对广义非线性比式和问题的等价问题使用指数变换及线性下界估计,建立等价问题的松弛线性规划,通过对松弛线性规划可行域的细分及一系列线性规划的求解达到提出的一种确定型全局优化算法,理论上证明收敛到问题的全局最优解·实验表明,该算法具有可行性、有效性. By the exponential transformations and linear underestimating for the equivalence form of the sum of general- ized nonlinear ratios problems, the linear relaxation programming of equivalence problem is established. Through successive- ly refining the feasible region of linear relaxation problem and solving a sequence of linear relaxation programming problems, a proposed determined global optimization algorithm is theoretically proved to convergent to the global solution of prime problem and is indicated feasible and efficient on numerical results.
作者 袁瑰霞 申培萍
机构地区 河南师范大学数学与信息科学学院
出处 《周口师范学院学报》 CAS 2006年第5期12-14,33,共4页 Journal of Zhoukou Normal University
基金 国家社会科学基金资助项目(No.05XRK008) 河南省自然科学基金资助项目(No.0511011500) 河南省软科学研究计划项目(No.0513030920) 河南省教育厅自然科学基金资助项目(No.2004110007)
关键词 全局优化 非线性比式和 线性松弛 分支定界 global optimization sum of generalized nonlinear ratios linear relaxation, 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3

  • 1Bensen H P.Globally optimization algorithm for the nonlinear sum of ratios problem[J].Journal of Optimization Theory and Applications,2002,112(1):1-29.
  • 2Tuy H,Thach P T,Konno H.Optimization of polynomial fractional functions[J].Journal of Global Optimization,2004,29:19-44.
  • 3Horst R,Tuy H.Global Optimization:Deterministic Approaches[M].3rd ed.Berlin:Springer Verlag,1997.

同被引文献16

  • 1Hestenes M R. Multiplier and gradient methods[J]. Journal of optimization Theory and Application, 1969(4) .. 303 - 320.
  • 2Powell M J D. A method for nonlinear constraints in minimization problems in optimization[M]. R. Fletcher(ed. ). New York, NY ~ Academic Press, 1969 .. 283 - 298.
  • 3Andreani R, Birgin G E, Martinez J M,et al. Augmented Lagrangian methods under the Constant Positive Linear De- pendence constraint qualification[J]. Mathematical Programming, 2008, 111:5 -32.
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  • 8Andreani R,Birgin E G, Martinez J M, et al. On augmented Lagrangian methods with general lower-level constraint[J]. SIAM J Optim, 2007, 1:8~1286- 1309.
  • 9Birgin E G,Castillo R A, Martnes J M. Numerical comparison of augmented Lagrangian algorithms for non convex problems, computer[J].Optim. Appl. ,2005, 31:31 - 55.
  • 10Luo H Z,Sun X L, Li D. On the convergence of augmented Lagrangian methods for constrained global optimization[J]. SIAM J Optim,2007, 18:1209 - 1230.

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周口师范学院学报
2006年 第5期

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