MINLP formulations for continuous piecewise linear function fitting

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

doi:10.1007/s10589-021-00268-5

MINLP formulations for continuous piecewise linear function fitting

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

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	223-233
Number of pages	11
Journal	Computational Optimization and Applications
Volume	79
Issue number	1
DOIs	https://doi.org/10.1007/s10589-021-00268-5
State	Published - 1 May 2021
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1007/s10589-021-00268-5

Cite this

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title = "MINLP formulations for continuous piecewise linear function fitting",

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.",

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AU - Goldberg, Noam

AU - Rebennack, Steffen

AU - Kim, Youngdae

AU - Krasko, Vitaliy

AU - Leyffer, Sven

PY - 2021/5/1

Y1 - 2021/5/1

N2 - 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.

AB - 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.

KW - Branch-and-bound

KW - Linear spline regression

KW - Mixed-integer nonlinear program

KW - Reformulation

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MINLP formulations for continuous piecewise linear function fitting

Abstract

Keywords

ASJC Scopus subject areas

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