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The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

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Abstract.

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values.

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi e Informatica, IASI-CNR, Viale Manzoni 30, I-00185 Roma, Italy, e-mail: rinaldi@iasi.rm.cnr.it, , , , , , IT

    Giovanni Rinaldi

  2. Institut für Mathematik, Universität Freiburg, D-79104 Freiburg im Breisgau, Germany, e-mail: uvo@mathematik.uni-freiburg.de, , , , , , DE

    Ulrich Voigt

  3. Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, and Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria, e-mail: g.j.woeginger@math.utwente.nl, , , , , , NL

    Gerhard J. Woeginger

Authors
  1. Giovanni Rinaldi
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  2. Ulrich Voigt
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  3. Gerhard J. Woeginger
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Additional information

Received: August 2001 / Accepted: January 2002¶Published online March 27, 2002

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Rinaldi, G., Voigt, U. & Woeginger, G. The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs. Math. Program. 93, 77–86 (2002). https://doi.org/10.1007/s101070200298

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  • DOI: https://doi.org/10.1007/s101070200298