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A complementary variant of Lemke's method for the linear complementary problem

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Abstract

An algorithm for the linear complementarity problem is developed which uses principal pivots only. The algorithm is shown to be equivalent to Lemke's algorithm. The advantage of the proposed algorithm is that infeasibility tests may be made after each principal pivot. One such test is equivalent to a check whether the matrix satisfies the “plus” condition of copositive plus matrices or the condition of classL 2 of Eaves.

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Research was partially supported by a grant from the Canadian National Research Council.

The author is indebted to the referees for drawing his attention to the related method developed by McCammon [7], which was not considered in an earlier version.

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van de Panne, C. A complementary variant of Lemke's method for the linear complementary problem. Mathematical Programming 7, 283–310 (1974). https://doi.org/10.1007/BF01585528

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  • DOI: https://doi.org/10.1007/BF01585528

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