MINLP formulations for continuous piecewise linear function fitting

Noam Goldberg, Steffen Rebennack, Youngdae Kim, Vitaliy Krasko, Sven Leyffer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)223-233
Number of pages11
JournalComputational Optimization and Applications
Issue number1
StatePublished - May 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).


  • Branch-and-bound
  • Linear spline regression
  • Mixed-integer nonlinear program
  • Reformulation


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