MINLP formulations for continuous piecewise linear function fitting

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 linea...

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Vydáno v:Computational optimization and applications Ročník 79; číslo 1; s. 223 - 233
Hlavní autoři: Goldberg, Noam, Rebennack, Steffen, Kim, Youngdae, Krasko, Vitaliy, Leyffer, Sven
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer US 01.05.2021
Springer Nature B.V
Témata:
Branch-and-bound
Continuity (mathematics)
Convex and Discrete Geometry
Linear functions
Linear spline regression
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Mixed-integer nonlinear program
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Reformulation
Statistics
Linear spline regression
Branch-and-bound
Mixed-integer nonlinear program
Reformulation
ISSN:1573-2894, 0926-6003, 1573-2894
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-021-00268-5