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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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