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一个新的拟牛顿信赖域算法 被引量：1

A New Method on Modified Quasi-Newton Trust Region
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摘要 提出了一种新的修正拟牛顿信赖域算法.算法同时利用函数值信息和梯度信息构造信赖域子问题,既可保持信赖域子问题海森矩阵的正定性,又能改善算法的数值执行.在一定假设的条件下,证明了算法的全局收敛性,并通过数值实验表明了提出算法的有效性. A new trust region method based on the modified quasi-Newton equation are proposed.The presented algorithm uses available gradient and function information to build trust region subproblem,which can not only make sure the positive-definite for Hessian matrix of trust region subproblem but also improve numerical implementation.Under some suitable conditions,a global convergence theorem is established.Numerical experiments show that the presented algorithm is efficient.
作者 李文钰 路云龙
机构地区 北华大学数学学院
出处 《北华大学学报（自然科学版）》 CAS 2009年第5期385-388,共4页 Journal of Beihua University（Natural Science）
基金 吉林省教育厅“十一五”科学研究项目(2008-129)
关键词 信赖域方法 修正拟牛顿方法 全局收敛性 Trust region Modified quasi-Newton equation Global convergence
分类号 O221.2 [理学—运筹学与控制论]
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参考文献8

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同被引文献17

  • 1柯小伍,韩继业.一类新的信赖域算法的全局收敛性[J].应用数学学报,1995,18(4):608-615. 被引量：31
  • 2Nlcedal J, Yuan Y X. Combining trust region and linear search techniques[R]. Technical Report,NAM06,Dept of Computer Science,Northwestern University Illinois,USA,1991.
  • 3Nlcedal J, Yuan Y X. Combining trust region and linear search techniques[J], Advances in Nonlin-ear Programming,1998:153 - 175.
  • 4Michael Gertz E. A quasi-Newton trust-region method[J]. Mathematical Programming, 2004,100(3).447 - 470.
  • 5Deng N Y,Xiao Y, Zhou F J. A nonmonotonic trust region algorithm[J], Journal of optimizationTheory and Applications, 1993,76(2) :259 - 285.
  • 6Toint P. A non-monotonic trust-region algorithm for nonlinear optimization subject to convex con-strains[J], Mathematical Programming, 1997,77(1) :69 - 94.
  • 7Masoud Ahookhosh, Key van Amini.Somayeh Bahrami. A class of nonmonotone Armijo-type linesearch method for unconstrained optimization[J]. Optimization,2012,61(4) :387 - 404.
  • 8Grippo L, Lampariello F, Lucidi S. A non-monotone line search technique for Newton’s method[J]. SIAM J,Numer Anal,1986,23(4) :707 - 716.
  • 9Zhang H C. Hager W W. A non-monotone line search technique and its application to uncon-strained optimization[J]. SIAM J Optim,2004,14(4) : 1043 - 4056.
  • 10Broyden C G. The Convergence of class of double rank mininization algorithms parts I and parts II[J]. Journal of the Institute of Mathematics and Applications, 1977(7) : 76 - 90.

引证文献1

北华大学学报（自然科学版）
2009年 第5期

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