On Some Properties of $K$- type Block Matrices in the context of Complementarity Problem

TL;DR

This paper introduces new classes of $K$-type block matrices, explores their properties, and demonstrates how they facilitate solving linear complementarity problems efficiently.

Contribution

It defines block triangular and hidden block triangular $K$-matrices, proving their key properties and their suitability for linear complementarity problem solutions.

Findings

Block triangular $K$-matrices satisfy the least element property.

Hidden block triangular $K$-matrices are $Q_0$ and compatible with Lemke's algorithm.

Solution of LCP with $K$-type block matrices reduces to linear programming.

Abstract

In this article we introduce $K$-type block matrices which include two new classes of block matrices namely block triangular $K$-matrices and hidden block triangular $K$-matrices. We show that the solution of linear complementarity problem with $K$-type block matrices can be obtained by solving a linear programming problem. We show that block triangular $K$-matrices satisfy least element property. We prove that hidden block triangular $K$-matrices are $Q_0$ and processable by Lemke's algorithm. The purpose of this article is to study properties of $K$-type block matrices in the context of the solution of linear complementarity problem.