A Polynomial-Time Algorithm for the Tridiagonal and Hessenberg P-Matrix Linear Complementarity Problem

TL;DR

This paper presents a polynomial-time dynamic programming algorithm for solving the linear complementarity problem specifically for tridiagonal and Hessenberg P-matrices, expanding the classes of matrices for which efficient solutions are known.

Contribution

The paper introduces a new polynomial-time algorithm tailored for tridiagonal and Hessenberg P-matrices in the linear complementarity problem, filling a gap in existing tractable matrix classes.

Findings

Algorithm solves LCP with these matrices in polynomial time

Tridiagonal P-matrices are not contained in previously known tractable classes

Provides a new approach for specific matrix structures in LCPs

Abstract

We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of them contains all tridiagonal P-matrices.