The Kantorovich theorem for nonlinear complementarity problems
type: Item
instance of: scholarly article
title: The Kantorovich theorem for nonlinear complementarity problems
zbMATH Open document ID: 0760.65068
published in: Chinese Science Bulletin
publication date: 1993-01-16T00:00:00Z
review text: In this note the following nonlinear complementarity problem is considered: Let \(K=\mathbb{R}^ n_ +\), \(F\in K\to\mathbb{R}^ n\). Find \(x\in K\) such that \(F(x)\geq 0\), \((F(x),x)=0\). This problem is equivalent to the variational inequality: Find \(x\in K\) such that \((F(x),y-x)\geq 0\), \(\forall y\in K\). The authors establish some basic results of the semilocal convergence theory of Newton and quasi-Newton methods for solving the given nonlinear complementarity problem.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 95726
zbMATH Keywords: nonlinear complementarity problem
zbMATH Keywords: variational inequality
zbMATH Keywords: semilocal convergence
zbMATH Keywords: quasi-Newton methods
author: Shuzi Zhou
author: Qin-Rong Yan
reviewed by: Hans Benker
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 95726