Identification of the optimal active set in a noninterior continuation method for LCP
type: Item
instance of: scholarly article
title: Identification of the optimal active set in a noninterior continuation method for LCP
zbMATH Open document ID: 1036.90070
DOI: 10.1023/A:1023065422836
published in: Journal of Global Optimization
publication date: 2004-02-12T00:00:00Z
review text: The authors investigate convergence properties of a modification of the non-interior point method continuation method suggested by \textit{J. Burke} and \textit{S. Xu} [J. Optimization Theory. Appl. 112, 53--76 (2002; Zbl 1049.90097)] for the standard linear complementarity problem. It is shown that the method determines the optimal active set of this problem in a finite number of iterations if the basic matrix is \(P\) and the problem is not degenerate. Namely, the method requires \(O( \rho \log (\beta_{0} \mu_{0} / \tau))\) iterations, where \(\beta_{0}\) is the width of the initial neighborhood, \(\mu_{0}\) is the initial smoothing parameter, and the constants \(\rho\) and \(\tau\) depend on the properties of the problem.
reviewed by: Igor V. Konnov
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 2041245
zbMATH Keywords: linear complementarity
zbMATH Keywords: continuation method
zbMATH Keywords: optimal active set
author: Naihua Xiu
author: Jianzhong Zhang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2041245