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
Recommended Citation
Dubey, Dipti and Neogy, S. K., "On generalizations of positive subdefinite matrices and the linear complementarity problem" (2018). Journal Articles. 1196.
https://digitalcommons.isical.ac.in/journal-articles/1196