GLOBAL LINEAR AND QUADRATIC ONE-STEP SMOOTHING NEWTON METHOD FOR VERTICAL LINEAR COMPLEMENTARITY PROBLEMS  

作　　者：张立平 高自友 

机构地区：[1]Department of Methematical Sciences, Tsinghua University [2]School of Traffic and Transportation, Northern Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2003年第6期738-746,F003,共10页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina (1 0 2 0 1 0 0 1 ) ;theNationalOutstandingYoungInvestigatorGrant (70 2 2 50 0 5)

摘　　要：A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).

关 键 词：vertical linear complementarity problems smoothing Newton method global linear convergence quadratic convergence 

分 类 号：O177.91[理学—数学]