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

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  • J. J. Júdice
  • F. M. Pires

Abstract

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 ∈ 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 ∈ P. We 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.

Suggested Citation

  • J. J. Júdice & F. M. Pires, 1990. "A bard‐type method for a generalized linear complementarity problem with a nonsingular m‐matrix," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 279-297, April.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:2:p:279-297
    DOI: 10.1002/1520-6750(199004)37:23.0.CO;2-V
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    1. van der Laan, G. & Talman, A.J.J., 1985. "An algorithm for the linear complementarity problem with upper and lower bounds," Other publications TiSEM fbcd28cb-a339-4fc5-844b-f, Tilburg University, School of Economics and Management.
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