\(Q\)-matrices and boundedness of solutions to linear complementarity problems
type: Item
instance of: scholarly article
title: \(Q\)-matrices and boundedness of solutions to linear complementarity problems
zbMATH Open document ID: 0831.90111
DOI: 10.1007/BF02190060
author: R. A. Danao
published in: Journal of Optimization Theory and Applications
publication date: 1996-02-22T00:00:00Z
review text: For a given matrix \(M\in \mathbb{R}^{n\times n}\) and a vector \(q\in \mathbb{R}^n\), the linear complementarity problem is that of finding \(w\), \(z\in \mathbb{R}^n\) such that \(w= Mz+ q\), \(w\geq 0\), \(z\geq 0\), \(w^T z= 0\). It has been previously established by \textit{O. L. Mangasarian} [Math. Program. Study 18, 153-166 (1982; Zbl 0487.90088)] that, if \(M\) is copositive plus, then the solution set of the complementarity problem is nonempty and bounded for each \(q\in \mathbb{R}^n\) iff \(M\) is a \(Q\)-matrix. The author has shown that this result also holds if \(M\) belongs to any of the classes of \(L_2\)-matrices, \(P_0\)-matrices, nonnegative matrices, and \(z\)-matrices.
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 698710
zbMATH Keywords: linear complementarity
zbMATH Keywords: \(P_ 0\)-matrices
zbMATH Keywords: \(z\)-matrices
MaRDI profile type: Publication
cites work: On the number of solutions to the complementarity problem and spanning properties of complementary cones
cites work: Some perturbation results for the Linear Complementarity Problem
cites work: Q4135216
cites work: Characterizations of bounded solutions of linear complementarity problems
cites work: Q5808749
cites work: The complementarity problem
cites work: The Linear Complementarity Problem
cites work: Some Perturbation Theorems for Q-Matrices
cites work: On the Alass of Complementary Cones and Lemke’s Algorithm
cites work: On the number of solutions to a class of linear complementarity problems
cites work: OnQ-matrices
cites work: A note onQ-matrices
cites work: On the uniqueness of solutions to linear complementarity problems
cites work: An example of a nonregular semimonotone \(Q\)-matrix
full work available at URL: https://doi.org/10.1007/bf02190060
OpenAlex ID: W2031135002
description: scientific article; zbMATH DE number 698710