Reduction of affine variational inequalities

Stephen M. Robinson ()
Additional contact information
Stephen M. Robinson: University of Wisconsin–Madison

Computational Optimization and Applications, 2016, vol. 65, issue 2, No 9, 493-509

Abstract: Abstract We consider an affine variational inequality posed over a polyhedral convex set in n-dimensional Euclidean space. It is often the case that this underlying set has dimension less than n, or has a nontrivial lineality space, or both. We show that when the variational inequality satisfies a well known regularity condition, we can reduce the problem to the solution of an affine variational inequality in a space of smaller dimension, followed by some simple linear-algebraic calculations. The smaller problem inherits the regularity condition from the original one, and therefore it has a unique solution. The dimension of the space in which the smaller problem is posed equals the rank of the original set: that is, its dimension less the dimension of the lineality space.

Keywords: Affine variational inequality; Coherent orientation; Complementarity; Lineality space; Normal map; Reduction; 49J53; 49J40; 49K40; 90C31; 90C33 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-015-9796-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:65:y:2016:i:2:d:10.1007_s10589-015-9796-7

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9796-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().