Components identification based method for box constrained variational inequality problems with almost linear functions
type: Item
instance of: scholarly article
title: Components identification based method for box constrained variational inequality problems with almost linear functions
zbMATH Open document ID: 1165.65037
author: Zhengyu Wang
published in: BIT
publication date: 2009-04-29T00:00:00Z
review text: For finding the solution \(x^{\ast}\) of a mixed complementarity problem in form of a variational inequality with box constraints \((y - x^{\ast})^T F(x^{\ast}) \geq 0 \;\; \forall y \in [l, u] \) and with almost linear functions \(F(x) = Mx + \varphi(x)\) an iterative algorithm is developed. The algorithm computes an approximate solution by solving at most \(n\) reduced systems of equations. Only the one of the smallest dimension has to be solved with high accuracy, the others are solved merely to identify some components of the solution. The performance of the algorithm is demonstrated numerically for a finite element discretized obstacle problem. The numerical results show that the algorithm is more efficient than the semi-smooth Newton method of \textit{C. Kanzow} and \textit{M. Fukushima} [Oper. Res. Lett. 23, No. 1--2, 45--51 (1998; Zbl 0941.90070)].
reviewed by: Bülent Karasözen
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 5549594
zbMATH Keywords: mixed complementarity problem
zbMATH Keywords: variational inequality
zbMATH Keywords: almost linear functions
zbMATH Keywords: obstacle problems
zbMATH Keywords: iterative algorithm
zbMATH Keywords: performance
zbMATH Keywords: finite element
zbMATH Keywords: numerical results
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: s10543-008-0202-z
OpenAlex ID: W2084183107
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DOI: 10.1007/S10543-008-0202-Z
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description: scientific article; zbMATH DE number 5549594