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求解非线性互补问题的光滑牛顿算法 被引量：2

A One-step Smoothing Newton Method for Nonlinear Complementarity Problem with P_0-function
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摘要 基于一个扰动的光滑双曲余弦函数,给出了求解P0-函数非线性互补问题的光滑牛顿算法,该算法在每次迭代只需要求解一次牛顿方程组,执行一次Amijo线搜索.在适当条件下,该算法全局收敛性和局部超线性收敛性也得到了证明. Based on the perturbed smoothing cosh function, is proposed a smoothing Newton method for nonlinear complementarity problem with a P0 -function. It solves only one linear system of equations and performs only one Armijo-type line search per iteration. The global convergence and the rate of convergence of the proposed algorithm is verified under mild conditions.
作者 唐嘉
机构地区 福建师范大学数学与计算机科学学院
出处 《福建师范大学学报（自然科学版）》 CAS CSCD 北大核心 2013年第6期18-22,66,共6页 Journal of Fujian Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(11201074)
关键词 非线性互补问题 一步光滑牛顿算法 局部收敛性 全局收敛性 nonlinear complementarity problem one-step smoothing Newton method global convergence local convergence
分类号 O224.2 [理学—运筹学与控制论]
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参考文献7

  • 1陈国庆,曹兵.箱约束变分不等式的一种新NCP-函数及其广义牛顿法[J].计算数学,2002,24(1):91-104. 被引量：17
  • 2Xu S.The global linear convergence of an infeasible non-interior path-following algorithm for complementarity problems with uniform P-functions[J].Math Prog,2000,87:501-517.
  • 3Chen B,Chen X,Kanzow C.A penalized Fischer-Burmeister NCP-function:theoretical investigate and numerical results[J].Mathematical Programming,2000,88:211-216.
  • 4Xiu N,Zhang J.Some recent advances in projection-type methods for variational inequalities[J].J Comput Appl Math,2003,152:559-585.
  • 5Zhen S Y,Yi Q.A cosh-based smoothing Newton method for P0 nonlinear complementarity problem[J].Nonlinear Analysis:Real World Applications,2011,12:875-884.
  • 6Ravindran G,Gowda M S.Regularization of P0-functions in box variational inequality problems[J].SIAM Journal on Optimization.2000,11:748-760.
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二级参考文献9

  • 1Nobuo Yamashita,Masao Fukushima. Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems[J] 1997,Mathematical Programming(3):469～491
  • 2Francisco Facchinei,Christian Kanzow. A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems[J] 1997,Mathematical Programming(3):493～512
  • 3Tecla Luca,Francisco Facchinei,Christian Kanzow. A semismooth equation approach to the solution of nonlinear complementarity problems[J] 1996,Mathematical Programming(3):407～439
  • 4Bintong Chen,Patrick T. Harker. A continuation method for monotone variational inequalities[J] 1995,Mathematical Programming(1-3):237～253
  • 5Baichun Xiao,Patrick T. Harker. A nonsmooth Newton method for variational inequalities, I: Theory[J] 1994,Mathematical Programming(1-3):151～194
  • 6Jong-Shi Pang,Steven A. Gabriel. NE/SQP: A robust algorithm for the nonlinear complementarity problem[J] 1993,Mathematical Programming(1-3):295～337
  • 7P. K. Subramanian. Gauss-Newton methods for the complementarity problem[J] 1993,Journal of Optimization Theory and Applications(3):467～482
  • 8Liqun Qi,Jie Sun. A nonsmooth version of Newton’s method[J] 1993,Mathematical Programming(1-3):353～367
  • 9Patrick T. Harker,Jong-Shi Pang. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications[J] 1990,Mathematical Programming(1-3):161～220

共引文献16

同被引文献11

引证文献2

二级引证文献2

福建师范大学学报（自然科学版）
2013年 第6期

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