The dual gap function for variational inequalities
type: Item
instance of: scholarly article
title: The dual gap function for variational inequalities
zbMATH Open document ID: 1048.49007
author: Changyu Wan
author: Jianzhong Zhang
author: Naihua Xiu
published in: Applied Mathematics and Optimization
publication date: 2003-12-16T00:00:00Z
review text: The dual gap function \(G\) of a variational inequality problem (VIP) was introduced by Marcotte and Zhu. By using some characterizations of \(G\), they studied the relationship among a global error bound, weak sharpness of the solution set, minimum principle sufficiency (MPS) property and finite termination of descent algorithms for the solution of a VIP. Most of their main results require the assumption that the function \(F\) which defines the VIP is pseudo-monotone\(^+\) and the set \(X\) on which the VIP is defined is compact. However, these two conditions are rather strong, reducing too much the class of considered problems. By giving some new characterization of the directional derivative and subdifferential properties of the dual gap function, the authors relax these conditions. As a result one gets a better understanding of the notions of global error bound, weak sharpness of the solution set and MPS property for a VIP.
reviewed by: S. Z. Németh
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 2018229
zbMATH Keywords: variational inequalities
zbMATH Keywords: dual gap function
zbMATH Keywords: directional derivative
zbMATH Keywords: subdifferential
zbMATH Keywords: error bound
zbMATH Keywords: weak sharpness
MaRDI profile type: Publication
full work available at URL: s00245-003-0771-9
OpenAlex ID: W1892757353
DOI: 10.1007/S00245-003-0771-9
description: scientific article; zbMATH DE number 2018229