Iterative methods for nonlinear quasi complementarity problems
type: Item
instance of: scholarly article
title: Iterative methods for nonlinear quasi complementarity problems
zbMATH Open document ID: 0623.90081
DOI: 10.1155/S0161171287000401
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46201
review text: The author studies the generalized nonlinear quasi complementarity problem of finding \(u\in K(u)\) such that \(Tu\in K^*(u)\) and \((u- m(u),Tu)=0\), where m is a point-to-point mapping. T is a nonlinear continuous mapping from a real Hilbert space H into itself, \(K^*(u)\) is the polar cone of the convex cone K(u) in H, and (.,.) denotes the inner product. He gives an approximate solution to this problem by the following iterative scheme: (i) Given \(u_ 0\in H\). (ii) \(u_{n+1}=m(u_ n)+P_ k[u_ n-\rho (Tu_ n)-m(u_ n)]\), \(n=0,1,2,3,...\), where \(P_ k\) is the projection of H into K, and \(\tau >0\) is required to satisfy the following conditions: \[ | \rho - \frac{\alpha}{\beta^ 2}| < \frac{\sqrt{\alpha^ 2-4\beta^ 2(\gamma -\gamma^ 2)}}{\beta^ 2},\quad \gamma < 1/2 \text{ and } \alpha \geq 2\beta \sqrt{\gamma -\gamma^ 2}. \]
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M20
zbMATH DE Number: 4012342
zbMATH Keywords: variational inequalities
zbMATH Keywords: convergence criteria
zbMATH Keywords: generalized nonlinear quasi complementarity problem
zbMATH Keywords: real Hilbert space
zbMATH Keywords: polar cone
author: Muhammad Aslam Noor
reviewed by: Z. J. Liu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4012342