A bard-type method for a generalized linear complementarity problem with a nonsingular m-matrix

✍ Scribed by J. J. Júdice; F. M. Pires

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 795 KB
• Volume: 37
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/1520-6750(199004)37:2<279::aid-nav3220370207>3.0.co;2-v

✦ Synopsis

In this article we 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 M has positive principal minors ( M E P). We 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. We 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 M E P. We show that if M E 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.