Mixed Integer Linear Programming (MILP) models are commonly used to model indicator constraints, which either hold or are relaxed depending on the value of a binary variable. Classification problems with Ramp Loss functions are an important application of such models. Mixed Integer Nonlinar Programming (MINLP) models are usually dismissed because they cannot be solved as efficiently. However, we show here that a subset of classification problems can be solved much more efficiently by a MINLP model with nonconvex constraints. This calls for a reconsideration of the modeling of these indicator constraints.
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