A block principal pivoting algorithm for the vertical generalized linear complementarity problem

A. A. Ebiefung, L. M. Fernandes, J. Júdice and M. Kostreva

Abstract

The Vertical Generalized Linear Complementarity Problem (VGLCP) is an extension of the well-known Linear Complementarity Problem (LCP) that has been discussed in the literature and has found many interesting applications in the past several years. A Block Principal Pivoting (BPP) algorithm was designed for finding the unique solution of the LCP when the matrix of this problem is a P-matrix and shown to be quite efficient for solving large-scale LCPs. In this paper, we introduce an extension of this BPP algorithm for finding the unique solution of the VGLCP when its matrix is a vertical block P-matrix. A Least-Index Single Pivoting (LISPP) algorithm is used as a safeguard to guarantee convergence for the BBP algorithm in a finite number of iterations. Computational experiments with a number of VGLCP test problems indicate that the new BPP algorithm is quite efficient for computing the unique solution of large-scale VGLCPs with vertical block P-matrices in practice.