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Randomized pivot algorithms for P-matrix linear complementarity problems

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Abstract.

We study orientations of the n-cube that come from simple principal pivot algorithms for the linear complementarity problem with a P-matrix. We show that these orientations properly generalize those that are obtained from linear objective functions on polytopes combinatorially equivalent to the cube. The orientations from LCP with a P-matrix may admit directed cycles. We give a sequence of problems on which the algorithm RANDOM-EDGE performs very badly.

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Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, Virginia, 22030, USA, , , , , , US

    Walter D. Morris jr.

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  1. Walter D. Morris jr.
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Received: February 12, 2001 / Accepted: September 9, 2001¶Published online April 12, 2002

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Morris jr., W. Randomized pivot algorithms for P-matrix linear complementarity problems. Math. Program. 92, 285–296 (2002). https://doi.org/10.1007/s101070100268

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  • DOI: https://doi.org/10.1007/s101070100268

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