Quadratic one-step smoothing Newton method for \(P_{0}\)-LCP without strict complementarity.
type: Item
instance of: scholarly article
title: Quadratic one-step smoothing Newton method for \(P_{0}\)-LCP without strict complementarity.
zbMATH Open document ID: 1049.65054
DOI: 10.1016/S0096-3003(02)00234-5
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: The linear complementarity problem with a matrix having all principal minors nonnegative is equivalent to a system of equations with Kanzow's smoothing function. This is solved by Newton's method involving only one linear system and only one Armijo-type line search. The algorithm has local quadratic convergence under nonsingularity condition. Boundedness of iterations is guaranteed by another condition. A comparison with methods from the literature is given and it is claimed that the algorithm has stronger convergence properties under weaker assumptions than many others.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 1978089
zbMATH Keywords: linear complementarity problem
zbMATH Keywords: Newton's method
zbMATH Keywords: global convergence
zbMATH Keywords: quadratic convergence
zbMATH Keywords: smoothing
zbMATH Keywords: line search
author: Liping Zhang
author: Ziyou Gao
reviewed by: Sanjo Zlobec
MaRDI profile type: Publication
cites work: A comparison of large scale mixed complementarity problem solvers
cites work: A non-interior predictor-corrector path following algorithm for the monotone linear complementarity problem
cites work: The global linear convergence of a noninterior path-following algorithm for linear complementarity problems
cites work: Q4252815
cites work: A Non-Interior-Point Continuation Method for Linear Complementarity Problems
cites work: Superlinear noninterior one-step continuation method for monotone LCP in the absence of strict complementarity.
cites work: A Global and Local Superlinear Continuation-Smoothing Method forP0andR0NCP or Monotone NCP
cites work: Smooth Approximations to Nonlinear Complementarity Problems
cites work: A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen--Mangasarian Smoothing Functions
cites work: Smoothing methods for convex inequalities and linear complementarity problems
cites work: A class of smoothing functions for nonlinear and mixed complementarity problems
cites work: Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
cites work: On the convergence of a block successive over-relaxation method for a class of linear complementarity problems
cites work: A special newton-type optimization method
cites work: Weak univalence and connectedness of inverse images of continuous functions
cites work: The non-interior continuation methods for solving the \(P_0\) function nonlinear complementarity problem
cites work: Sub-quadratic convergence of a smoothing Newton algorithm for the \(P_0\)- and monotone LCP
cites work: Global convergence of a class of non-interior point algorithms using Chen-Harker-Kanzow-Smale functions for nonlinear complementarity problems
cites work: Some Noninterior Continuation Methods for Linear Complementarity Problems
cites work: A new approach to continuation methods for complementarity problems with uniform \(P\)-functions
cites work: Jacobian Smoothing Methods for Nonlinear Complementarity Problems
cites work: Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
cites work: A nonsmooth version of Newton's method
cites work: A Regularized Smoothing Newton Method for Box Constrained Variational Inequality Problems with P0-Functions
cites work: A Smoothing Newton Method for Extended Vertical Linear Complementarity Problems
cites work: A smoothing Newton method for general nonlinear complementarity problems
cites work: A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
cites work: Improving the convergence of non-interior point algorithms for nonlinear complementarity problems
cites work: Regularization of \(P_{0}\)-functions in box variational inequality problems
cites work: Q3816922
cites work: Solving variational inequality problems via smoothing-nonsmooth reformulations
cites work: A regularization Newton method for solving nonlinear complementarity problems
cites work: Q4762533
cites work: Q4252835
full work available at URL: s0096-3003(02)00234-5
OpenAlex ID: W2023913568
description: scientific article; zbMATH DE number 1978089