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

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. Key words. non-linear optimization

• Type: Journal
• Year: 2002
• Where: MP
• Authors: Giovanni Rinaldi, Ulrich Voigt, Gerhard J. Woeginger
• Keywords: Integer Program, MP 2002, Non-linear Mixed Integer, NP-hard Problem