We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. https://doi.org/10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

我们考虑由Goldberg等人提出的非凸混合整数非线性规划（MINLP）模型。（2014年Compute Optim Appl 58：523–541。https：//doi.org/10.1007/s10589-014-9647-y）用于分段线性函数拟合。我们表明，此MINLP模型不完整，可能会产生不是函数图的分段线性曲线，因为它错过了一组必要的约束。我们提供了两个反例来说明这种效果，并提出了三种替代模型来纠正此行为。我们研究了这些模型之间的理论关系，并评估了它们的计算性能。