A block principal pivoting algorithm for vertical generalized LCP with a vertical block P-matrix

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 Principal Pivoting (LISPP) algorithm is used as a safeguard to guarantee convergence for the BPP 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.