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article · Computational Optimization and Applications · 2021

MINLP formulations for continuous piecewise linear function fitting

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

Cited by 8Open access

Abstract

Abstract We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 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.

Cite this paper

APA 7

Goldberg, N., Rebennack, S., Kim, Y., Krasko, V., & Leyffer, S. (2021). MINLP formulations for continuous piecewise linear function fitting. Computational Optimization and Applications, 79(1), 223–233. https://doi.org/10.1007/s10589-021-00268-5

MLA 9

Goldberg, Noam, et al. “MINLP formulations for continuous piecewise linear function fitting.” Computational Optimization and Applications, vol. 79, no. 1, 2021, pp. 223–33, https://doi.org/10.1007/s10589-021-00268-5.

Chicago

Goldberg, Noam, Steffen Rebennack, Youngdae Kim, Vitaliy Krasko, and Sven Leyffer. 2021. “MINLP formulations for continuous piecewise linear function fitting.” Computational Optimization and Applications 79 (1): 223–33. https://doi.org/10.1007/s10589-021-00268-5.

Harvard

Goldberg, N. et al. (2021) ‘MINLP formulations for continuous piecewise linear function fitting’, Computational Optimization and Applications, 79(1), pp. 223–233. Available at: https://doi.org/10.1007/s10589-021-00268-5.

BibTeX
@article{goldberg2021minlp,
  title = {{MINLP formulations for continuous piecewise linear function fitting}},
  author = {Goldberg, Noam and Rebennack, Steffen and Kim, Youngdae and Krasko, Vitaliy and Leyffer, Sven},
  journal = {Computational Optimization and Applications},
  volume = {79},
  number = {1},
  pages = {223--233},
  year = {2021},
  doi = {10.1007/s10589-021-00268-5}
}

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