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求解非线性方程组的非单调滤子算法 被引量：3

A Nonmonotone Filter Method for Nonlinear Equations
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摘要 提出了一个新的求解非线性方程组的滤子算法,首先把非线性方程组的求解转化成一个非线性优化问题,然后借助非单调技术和滤子技术求解该问题,从而得到了原方程组的解.在适当的条件下,证明了该算法的全局收敛性,初步的数值试验表明了该算法的有效性. This paper presents a new filter method for solving nonlinear equations. First, this problem is transformed into a nonlinear optimization. Then, it solves this question with the aid of nonmonotone technology and filter technology, and thus obtains a solution of the original nonlinear equation. Under reasonable conditions, it shows the global convergence properties. Preliminary numerical tests have proved the efficiency of the approach.
作者 黎维清 濮定国
机构地区 同济大学数学系
出处 《云南民族大学学报（自然科学版）》 CAS 2010年第4期253-256,共4页 Journal of Yunnan Minzu University:Natural Sciences Edition
基金 国家自然科学基金(10771162)
关键词 非线性方程组 滤子 非单调技术 全局收敛性 nonlinear equations filter nonmonotone technology global convergence
分类号 O221.2 [理学—运筹学与控制论]
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参考文献9

  • 1WACHETER A,BIEGLER L T.Line search filter methlds for nonlinear programming:motivation and global convergence[J].SIAM Journal on Optimization,2005,16:1-31.
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同被引文献27

  • 1HANS P.A global convergent method for nonlinear programing[J].Optim Theory Appl 1997,(22):297 -309.
  • 2POWELL M J D.A fast algorithm for nonlinear constrained optimization calculations,in:G.A.Waston (Ed.),Proceedings of the 1977 Dundee Biennial Conference on Numerical Analysis[M].Springer,Berlin,1978.
  • 3POWELL M J D.The convergence of variable metric methods for nonlinear constrained optimizationcalculations,in:O.L.Mangasarian,R.R.Meyer,S.M.Robinson (Eds.),Nonlinear Programming[M].Vol.3,Academic Press,New York,1978.
  • 4FLETCHER R,LEY ER S.Nonlinear programming without a penalty function[J].Mathematical Program-ming,2002,91(2):239 -269.
  • 5FLETCHER R,LEY ER S,TOINT P.On the global convergence of a filter-SQP algorithm[J].SIAM Jounalon Optimization,2002,(1):44-59.
  • 6FLETCHER R,GOULD N I M,TOINT P,et al.Global convergence of a trust region -lter-SQPmethod,SIAM Journal on Optimization[J].2002,13 (3):635-659.
  • 7GONZAGA C C,KARAS E,VANTI M.A globally convergent filter method for nonlinear program-ming[J].SIAM Journal on Optimization,2003,14(3):646-669.
  • 8RIBEIRO A A,KARAS E W,GONZAGA C C.Global convergence of filter methods for nonlinearprogramming,Technical report[R].Department of Mathematics,Federal University of Paran.a,Brazil,2006.
  • 9GOULD N I M,TOINT Ph L.Global convergence of a non-monotone trust-region filter algorithmfor nonlinear programming[R].Numerical Analysis Report RAL-TR-2003-003,Rutherford AppletonLaboratory,UK,2003.
  • 10GILL Philip E,MURRAY Walter,MICHAEL A.Saunders,An SQP Algorithm for Large-Scale ConstrainedOptimization[J].SIAM,Rev.2005,(47):99-131.

引证文献3

二级引证文献3

云南民族大学学报（自然科学版）
2010年 第4期

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