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

J. J. Júdice and F. M. Pires

Naval Research Logistics (NRL), 1990, vol. 37, issue 2, 279-297

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.

Date: 1990
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https://doi.org/10.1002/1520-6750(199004)37:23.0.CO;2-V

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:37:y:1990:i:2:p:279-297

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