A new subclass of Q0-matrix in linear complementarity theory
Article Type
Research Article
Publication Title
Linear Algebra and Its Applications
Abstract
In this article, we introduce a new matrix class L¯(d) (a subclass of Q0-matrices which are obtained as a limit of a sequence of L(d)-matrices) such that for any A in this class, a solution to LCP(q,A) exists if LCP(q,A) is feasible, and Lemke's algorithm will find a solution or demonstrate infeasibility. We present a counterexample to show that an L¯(d)-matrix need not be an L(d)-matrix. We also show that if A∈L¯(d), there is an even number of solutions for any nondegenerate vector q. An application of this new matrix class that arises from general quadratic programs and polymatrix games belongs to this class. Finally, we present an example related to the existence of equilibrium in polymatrix games.
First Page
64
Last Page
77
DOI
10.1016/j.laa.2022.04.011
Publication Date
8-15-2022
Recommended Citation
Singh, Gambheer; Neogy, S. K.; and Kumar, Promila, "A new subclass of Q0-matrix in linear complementarity theory" (2022). Journal Articles. 3004.
https://digitalcommons.isical.ac.in/journal-articles/3004