A Fast Algorithm for Solving a Class of the Linear Complementarity Problem in a Finite Number of Steps

Yamna Achik,Hajar Nafia,Youssef El Foutayeni,Imane Agmour,Asmaa Idmbarek,Victor Kovtunenko

doi:10.1155/2020/8881915

Abstract

The linear complementarity problem is receiving a lot of attention and has been studied extensively. Recently, El foutayeni et al. have contributed many works that aim to solve this mysterious problem. However, many results exist and give good approximations of the linear complementarity problem solutions. The major drawback of many existing methods resides in the fact that, for large systems, they require a large number of operations during each iteration; also, they consume large amounts of memory and computation time. This is the reason which drives us to create an algorithm with a finite number of steps to solve this kind of problem with a reduced number of iterations compared to existing methods. In addition, we consider a new class of matrices called the E-matrix.

Highlights

In the last decades, the complementarity problem has played a very important role in several domains
In [30], for solving the linear complementarity problem, Wang et al [31] propose an interior point method to find the solution of the linear complementarity problem, where the matrix is a real square hidden Z-matrix
It is a known fact that the linear complementarity problem LCPðq, MÞ is completely equivalent to solving the equation ðI + MÞx + ðI − MÞ ∣ x ∣ = q, where z = ∣x ∣ −x and w = ∣x ∣ +x

Summary

Introduction

The complementarity problem has played a very important role in several domains. In [30], for solving the linear complementarity problem, Wang et al [31] propose an interior point method to find the solution of the linear complementarity problem, where the matrix is a real square hidden Z-matrix In this context, we can see the works [31,32,33,34,35,36,37,38,39]. We formulate an algorithm that can solve the linear complementarity problem LCPðM, qÞ. This algorithm has a finite number of steps and converges to the solution.

Preliminary and Notations

Main Results

Numerical Examples

CHKS method

Conclusion