Benders decomposition for variational inequalities
type: Item
instance of: scholarly article
title: Benders decomposition for variational inequalities
zbMATH Open document ID: 0722.90024
DOI: 10.1007/BF01582257
author: Siriphong Lawphongpanich
author: Donald W. Hearn
published in: Mathematical Programming. Series A. Series B
publication date: 1990-01-01T00:00:00Z
review text: A variational inequality problem of the following type is considered: find \((x^*,y^*)\in S=\{(x,y)\); \(A_ 1x+A_ 2y=b\), \(x\in X\), \(y\in Y\}\) such that \(<C_ 1(x^*),x-x^*>+<C_ 2(y^*),y-y^*>\geq 0\) for every (x,y)\(\in S\). Here X and Y are subsets of finite-dimensional spaces, \(A_ 1\) and \(A_ 2\) are linear mappings, \(C_ 1\) and \(C_ 2\) are continuous mappings and \(<,>\) is the scalar product. The authors generalize the decomposition technique of Benders to the above problem with linear constraints. The approach is applied for the decomposition of the traffic assignment problem and is illustrated by a computational example.
reviewed by: Vladimir M. Veliov
Mathematics Subject Classification ID: 90B10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M27
Mathematics Subject Classification ID: 90B06
zbMATH DE Number: 4191375
zbMATH Keywords: variational inequality
zbMATH Keywords: linear constraints
zbMATH Keywords: traffic assignment
describes a project that uses: QPSOL
MaRDI profile type: Publication
cites work: Equilibria on a Congested Transportation Network
cites work: Sensitivity analysis for the asymmetric network equilibrium problem
cites work: Generalized variational inequalities
cites work: Generalized Benders decomposition
cites work: Q3905599
cites work: Q5591247
cites work: Q5585907
full work available at URL: https://doi.org/10.1007/bf01582257
OpenAlex ID: W2073315602
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description: scientific article; zbMATH DE number 4191375