More on hidden Z-matrices and linear complementarity problem

ABSTRACT

In this article, we study linear complementarity problem with hidden Z-matrix. We extend the results of Fiedler and Pták for the linear system in complementarity problem using game theoretic approach. We establish a result related to singular hidden Z-matrix. We show that for a non-degenerate feasible basis, linear complementarity problem with hidden Z-matrix has unique non-degenerate solution under some assumptions. The purpose of this paper is to study some properties of hidden Z-matrix.

KEYWORDS:

• Hidden Z-matrix
• linear complementary problem
• value of a matrix
• $P_0$-matrix
• $E_0$-matrix

AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 15A39
• 15B99

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors R. Jana and A. Dutta are thankful to the Department of Science and Technology, Govt. of India, INSPIRE Fellowship Scheme for financial support.