Sufficient matrices and the linear complementarity problem
type: Item
instance of: scholarly article
title: Sufficient matrices and the linear complementarity problem
zbMATH Open document ID: 0674.90092
DOI: 10.1016/0024-3795(89)90463-1
author: S. H. Smith
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: A new class of matrices, related to the linear complementarity problem (LCP), the so called ``row sufficient'' matrices, are introduced. Respectively, the transpose of such a matrix is called ``column sufficient''. Two important results are proved: (i) A matrix \(M\) is row sufficient iff for every \(q\in \mathbb R^n\) any Kuhn-Tucker-point of the associated quadratic program solves the LCP \((q,M)\); (ii) \(M\) is column sufficient iff for every \(q\in \mathbb R^n\) the LCP \((q,M)\) has a convex solution set. The connections with other well-known matrix classes in linear complementarity theory are also discussed.
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 4104740
zbMATH Keywords: row sufficient matrices
zbMATH Keywords: linear complementarity problem
zbMATH Keywords: column sufficient
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90463-1
OpenAlex ID: W1970000960
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Wikidata QID: Q56504900
description: scientific article; zbMATH DE number 4104740