### 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.

Original language | English |
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Pages (from-to) | 77-86 |

Journal | Mathematical programming |

Volume | 93 |

DOIs | |

Publication status | Published - 2002 |

### Keywords

- METIS-208619

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## Cite this

Rinaldi, G., Voigt, U., & Woeginger, G. (2002). The mathematics of playing golf, or: A new class of difficult non-linear mixed integer programs.

*Mathematical programming*,*93*, 77-86. https://doi.org/10.1007/s101070200298