A new continuation method for complementarity problems with uniform P- functions
type: Item
instance of: scholarly article
title: A new continuation method for complementarity problems with uniform P- functions
zbMATH Open document ID: 0673.90084
DOI: 10.1007/BF01582283
author: Shinji Mizuno
author: Toshihito Noma
author: Masakazu Kojima
published in: Mathematical Programming. Series A. Series B
publication date: 1989-01-01T00:00:00Z
review text: This paper formulates the (nonlinear) complementarity problem relative to a continuous mapping f as a problem of solving a system of equations defined by a particular mapping F from \(R_+^{2n}\) to \(R^ n_+\times R^ n\). It is shown that when f is a uniform P-function, the mapping F is a homeomorphism of \(R_+^{2n}\) to \(R^ n_+\times R^ n\). This forms the foundation of a continuation method for tracing the solution curve of the one-parameter family of systems of equations \(F(x,y)=tF(x^ 0,y^ 0)\) from an arbitrary point \((x^ 0,y^ 0)\in R_+^{2n}\) and \(t=1\) to \(t=0\).
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 4102834
zbMATH Keywords: nonlinear complementarity problem
zbMATH Keywords: uniform P-function
zbMATH Keywords: homeomorphism
zbMATH Keywords: continuation method
reviewed by: R. W. Cottle
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01582283
OpenAlex ID: W2038872086
description: scientific article; zbMATH DE number 4102834