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Solving more linear complementarity problems with Murty's bard-type algorithm

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Abstract

The linear complementarity problem (M|q) is to findw andz inR n such thatw−Mz=q,w≥0,z≥0,w t z=0, givenM inR n×n andq in . Murty's Bard-type algorithm for solving LCP is modeled as a digraph.

Murty's original convergence proof considered allq inR n andM inR n×n, aP-matrix. We show how to solve more LCP's by restricting the set ofq vectors and enlarging the class ofM matrices beyondP-matrices. The effect is that the graph contains an embedded graph of the type considered by Stickney and Watson wheneverM is a matrix containing a principal submatrix which is aP-matrix. Examples are presented which show what can happen when the hypotheses are further weakened.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina

    K. L. Dunlap (Graduate Student) & M. M. Kostreva (Professor)

Authors
  1. K. L. Dunlap
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  2. M. M. Kostreva
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Communicated by F. Zirilli

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Dunlap, K.L., Kostreva, M.M. Solving more linear complementarity problems with Murty's bard-type algorithm. J Optim Theory Appl 77, 497–522 (1993). https://doi.org/10.1007/BF00940447

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