Title

On generalizations of positive subdefinite matrices and the linear complementarity problem

Article Type

Research Article

Publication Title

Linear and Multilinear Algebra

Abstract

In this paper, we introduce the notion of generalized positive subdefinite matrices of level k by generalizing the definition of generalized positive subdefinite matrices introduced by Crouzeix and Komlósi in [Applied optimization. Vol. 59, Dordrecht: Kluwer Academic Publications; 2001. p. 45–63]. The main motivation behind this generalization is to identify new subclasses of row sufficient matrices [Cottle, Pang and Venkateswaran, Linear Algebra Appl. 1989;114/115:231–249] which are not a subclass of copositive matrices. We establish new sufficient conditions for a matrix to be a non-copositive P0 matrix and a non-copositive row sufficient matrix using the notion of generalized positive subdefinite matrices of level k. We present a new termination result for Lemke’s algorithm which supplements Jones’ result [Math Program. 1986;35:239–242].

First Page

2024

Last Page

2035

DOI

10.1080/03081087.2017.1383348

Publication Date

10-3-2018

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