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Linear complementarity problems solvable by A single linear program

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Abstract

It is shown that the linear complementarity problem of finding az inR n such thatMz + q ⩾ 0, z ⩾ 0 andz T (Mz + q) = 0 can be solved by a single linear program in some important special cases including those whenM or its inverse is a Z-matrix, that is a real square matrix with nonpositive off-diagonal elements. As a consequence certain problems in mechanics, certain problems of finding the least element of a polyhedral set and certain quadratic programming problems, can each be solved by a single linear program.

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Authors and Affiliations

  1. The University of Wisconsin, Madison, Wisc., USA

    O. L. Mangasarian

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  1. O. L. Mangasarian
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Additional information

Research supported by NSF Grant GJ 35292.

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Mangasarian, O.L. Linear complementarity problems solvable by A single linear program. Mathematical Programming 10, 263–270 (1976). https://doi.org/10.1007/BF01580671

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  • DOI: https://doi.org/10.1007/BF01580671

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