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Linear complementarity problems solvable by a polynomially bounded pivoting algorithm

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Mathematical Programming Essays in Honor of George B. Dantzig Part II

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 25))

Abstract

A sufficient condition is given under which the parametric principal pivoting algorithm will compute the unique solution to a linear complementarity problem defined by an n by n P-matrix in no more than n pivots. The condition is then shown to be satisfied by a P-matrix which has a hidden Z transpose and thus in particular, by an H-matrix with positive diagonals as well as by a strictly diagonally dominant matrix. The same condition is also shown to be sufficient for Lemke’s almost complementary algorithm to compute a solution to a linear complementarity problem defined by an n by n nondegenerate matrix in at most n+1 pivots. Finally, a polynomial testing procedure for the condition is described.

This research was initiated while the first author was visiting the Mathematics Research Center and the Department of Computer Sciences at the University of Wisconsin-Madison where he was partially supported by the United States Army under Contract No. DAAG29-80-C-0041.

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Authors and Affiliations

  1. School of Management, The University of Texas at Dallas, Box 830688, 75083-0688, Richardson, TX, USA

    J. S. Pang & R. Chandrasekaran

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  1. J. S. Pang
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  2. R. Chandrasekaran
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Richard W. Cottle

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Dedicated to Professor George B. Dantzig on the occasion of his seventieth birthday.

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© 1985 The Mathematical Programming Society, Inc.

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Pang, J.S., Chandrasekaran, R. (1985). Linear complementarity problems solvable by a polynomially bounded pivoting algorithm. In: Cottle, R.W. (eds) Mathematical Programming Essays in Honor of George B. Dantzig Part II. Mathematical Programming Studies, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121072

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  • DOI: https://doi.org/10.1007/BFb0121072

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00920-4

  • Online ISBN: 978-3-642-00921-1

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