MINLP formulations for continuous piecewise linear function fitting

Noam Goldberg (), Steffen Rebennack (), Youngdae Kim (), Vitaliy Krasko () and Sven Leyffer ()
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Noam Goldberg: Bar-Ilan University
Steffen Rebennack: Karlsruhe Institute of Technology
Youngdae Kim: Argonne National Laboratory
Vitaliy Krasko: Colorado School of Mines
Sven Leyffer: Argonne National Laboratory

Computational Optimization and Applications, 2021, vol. 79, issue 1, No 8, 223-233

Abstract: Abstract 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.

Keywords: Mixed-integer nonlinear program; Linear spline regression; Branch-and-bound; Reformulation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-021-00268-5

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