In this article the authors develop an extension of Murty’s Bard-type method for the solution of a generalized linear complementarity problem with upper bounds (BLCP) when its matrix N has positive principal minors (M∈P). They prove that the Bard-type algorithm converges to the unique solution of the BLCP when M is a P-matrix with nonpositive off-diagonal elements. The authors also study two special cases of the BLCP and prove that the Bard-type method is convergent to the unique solution of these BLCPs when N∈P. They show that if M∈NSM in these two cases, then the efficiency of the algorithm can be improved, by exploiting some properties of these problems. Computational experience with the Bard-type algorithm in the solution of large-scale BLCPs with sparse NSM maytrices is also included and shows the efficiency of this approach.
