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简单界约束非线性方程组的滤子信赖域法 被引量：1

A Filter-Trust-Region Method for Bound-Constrained Nonlinear Equations with Simple Bounds
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摘要 利用一种滤子信赖域方法讨论了简单界约束非线性方程组的求解问题,证明了该算法的全局收敛性,并且进行了数值试验,结果表明新算法非常有效. By a filter-trust-region algorithm the nonlinear optimization problems with simple bounds are discussed.This algorithm is shown to be global convergent.And numerical experiments are also reported,which shows that the algorithm is very effective.
作者 夏红卫 陈荣军
机构地区 常州工学院理学院
出处 《江西师范大学学报（自然科学版）》 CAS 北大核心 2009年第6期661-664,共4页 Journal of Jiangxi Normal University(Natural Science Edition)
基金 江苏省高校自然科学基金(06KJD110011)资助项目
关键词 界约束 滤子技巧 信赖域法 收敛 bound-constrained filter techniques trust-region method convergence
分类号 O224.2 [理学—运筹学与控制论]
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参考文献10

  • 1Conn A R, Gould N I M, Toint Ph L. Trust region methods [ M ]. Philadelphia: SIAM,2000.
  • 2Deng N Y,Xiao Y,Zhu D. A nonmonotone trust region algorithm[ J]. J Optimiz Theory Appl, 1993,76:259-285.
  • 3Toint Ph L. A nonmonotone trust region algorithm for nonlinear optimization subject to convex constraints [ J ]. Math Programming, 1997,77 : 69 -94.
  • 4Sun W. Nonmonotone trust-region method for optimization[ J ]. Appl Math Comput ,2004,156 : 159-174.
  • 5Fletcher R, Leyffer S. Nonlinear programming without a penalty function[ J ]. Math Programming,2002,91 (2) :239-269.
  • 6Yang Yu-fei, Qi Li-qun. Smoothing trust region methods for nonlinear complementarity problems with Po-functions [ J ]. Annals of Operations Researc h, 2005,133 ( 1 - 4 ) : 99 - 117.
  • 7Wachter A, Biegler L T. Line search filter methods for nonlinear programming :local convergence [ J ]. SIAM Journal on Optm,2005, 16(1) :32-48.
  • 8Chin C M, Rashid A H A, Mohamed Nor K. Global and local convergence of a filter line search method for nonlinear programming [ J]. Optimization Methods and Software,2007,22( 3 ) :365-390.
  • 9Gould N I M, Sainvitu C, Ph L Toint. A filter-trust-region method for unconstrained optimization [ J ]. SIAM Journal on Optimization, 2005,16 ( 2 ) : 341-357.
  • 10Hock W, Schittkowski K. Test example for nonlinear programming codes [ M ]. Berlin:Springer-Verlag, 1981.

同被引文献9

  • 1Lawrence C T, Tits A L. A computationally efficient feasible se-quential quadratic programming algorithm [J]. SIAM Journal on Optimization, 2001, 11 (4): 1092-1118.
  • 2Yuan Yaxiang. A review of trust region algorithms for optimiza- tion [C]//Ball J M, Hunt J C R. ICM99: Proceedings of the 4th International Congress on Industial and applied mathematics. Edinburgh: Oxford University Press, 2000: 271-282.
  • 3Powell M J D. Convergence properties of a class of minimization algorithms [C]//Mangassarian O L, Meyer R R, Robinson S M. Nonlinear Programming. New York: Academic Press, 1975: 1-27.
  • 4Chen Lifeng, Goldfarb D. Interior-point 12-penalty methods for nonlinear programming with strong global convergence proper- ties [J]. Math Programming, 2006, 108(1): 1-36.
  • 5Corm A R, Gould N I M, Orban D, et al. A primal-dual trust re- gion algorithm for non-convex nonlinear programming [J]. Math Programming, 2000, 87(2): 215-249.
  • 6Fletcher R, Leyffer S. Nonlinear programming without a penalty function [J]. Math Programming, 2002, 91(2): 239-269.
  • 7Conn A R, Gould N I M, Toint P L. Trust-region methods [M]. Philadephia: SIAM, 2000.
  • 8Conn A R, Gould N I M, Toint P L. Lancelot: a fortran package for large-scale nonlinear optimization [M]. New York: Springer, 1992.
  • 9夏红卫,陈荣军.一类等式约束非线性优化问题的信赖域新算法[J].数学的实践与认识,2010,40(20):131-137. 被引量：1

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江西师范大学学报（自然科学版）
2009年 第6期

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