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Solution of linear complementarity problems by linear programming

Part of the Lecture Notes in Mathematics book series (LNM,volume 506)

Abstract

The linear complementarity problem is that of finding an n x 1 vector z such that

Mz+q≧0, z≧0, zT (Mz+q)=0 where M is a given n x n real matrix and q is a given n x 1 vector. In this paper the class of matrices M for which this problem is solvable by a single linear program is enlarged to include matrices other than those that are z-matrices or those that have an inverse which is a z-matrix. (A Z-matrix is real square matrix with nonpositive offdiagonal elements.) Included in this class are other matrices such as nonnegative matrices with a strictly dominant diagonal and matrices that are the sum of a Z-matrix having a nonnegative inverse and the tensor product of any two positive vectors in Rn.

Research supported by NSF grants GJ35292 and DCR74-20584

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© 1976 Springer-Verlag

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Mangasarian, O.L. (1976). Solution of linear complementarity problems by linear programming. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080123

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  • DOI: https://doi.org/10.1007/BFb0080123

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07610-0

  • Online ISBN: 978-3-540-38129-7

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