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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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