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非线性方程的一个信赖域迭代算法 被引量:2

A TRUST REGION ITERATE ALGORITHM FOR NONLINEAR EQUATIONS
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摘要 对于信赖域子问题产生的搜索方向 ,利用一个给定的步长到达下一迭代点 ,证明了算法的全局收敛性 ,从而既避免了信赖域方法中在一次迭代多次求解信赖域子问题的困难 ,又避免了线搜索方法中为达到下一迭代点而多次调用函数值的计算 . A trust region trial step is utilized as a search direction and the next iteration is obtained via a given steplength. It not only avoids the difficulty of repeated solving trust region subproblems in an iterate in trust region algorithm but also avoids repeated computing function value in linear search algorithm.
出处 《曲阜师范大学学报(自然科学版)》 CAS 2004年第1期43-45,共3页 Journal of Qufu Normal University(Natural Science)
关键词 非线性方程 信赖域 迭代算法 全局收敛性 nonlinear equation trust region algorithm global convergence
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参考文献6

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同被引文献11

  • 1张荣,薛国民.修正的三次收敛的牛顿迭代法[J].大学数学,2005,21(1):80-82. 被引量:26
  • 2Grippo L,Lampariello F,Lucidi S.A nonmonotone line search technique for Newton's method[J].SIAM J Numer Anal,1986,23:707-716.
  • 3Chen X D,J Sun.Global convergence of a two-parameter family of conjugate gradient methods without line search[J].J Comput Appl Math,2002,146:37-45.
  • 4Sun J,Zhang J P.Global convergence of conjugate gradient methods without line search[J].Ann Oper Res,2001,103:161-173.
  • 5Zhang H C,Hager W W.A nonmonotone line search technique and its application to unconstrained optimization[J].SIAM J Optim,2004,14:1043-1056.
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  • 7Dennis J E,Schnabel R B.Numerical methods for unconstrained optimization and nonlinear equations[J].Prentice-Hall Inc,(Englewood Cliffs,NJ),1983.
  • 8Nocedal J,Yuan Y X.Combining trust region and line search techniques[C].in:Y.Yuan (Ed.),Advances in Nonlinear Programming Kluwer,1998,153-175.
  • 9Mo J T,Zhang K C,Wei Z X.A nonmonotone trust region method for unconstrained optimization[J].Appl Math Comput,2005,171(1):371-384.
  • 10杨帆,吴新元.关于不用计算导数的大范围收敛迭代法的注记[J].高等学校计算数学学报,2001,23(2):186-192. 被引量:14

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