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MINLP formulations for continuous piecewise linear function fitting

Author

Listed:
  • 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)

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.

Suggested Citation

  • Noam Goldberg & Steffen Rebennack & Youngdae Kim & Vitaliy Krasko & Sven Leyffer, 2021. "MINLP formulations for continuous piecewise linear function fitting," Computational Optimization and Applications, Springer, vol. 79(1), pages 223-233, May.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:1:d:10.1007_s10589-021-00268-5
    DOI: 10.1007/s10589-021-00268-5
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    References listed on IDEAS

    as
    1. Toriello, Alejandro & Vielma, Juan Pablo, 2012. "Fitting piecewise linear continuous functions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 86-95.
    2. Steffen Rebennack & Vitaliy Krasko, 2020. "Piecewise Linear Function Fitting via Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 507-530, April.
    3. Noam Goldberg & Youngdae Kim & Sven Leyffer & Thomas Veselka, 2014. "Adaptively refined dynamic program for linear spline regression," Computational Optimization and Applications, Springer, vol. 58(3), pages 523-541, July.
    4. Steffen Rebennack & Josef Kallrath, 2015. "Continuous Piecewise Linear Delta-Approximations for Univariate Functions: Computing Minimal Breakpoint Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 617-643, November.
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    Cited by:

    1. Nathan Sudermann-Merx & Steffen Rebennack, 2021. "Leveraged least trimmed absolute deviations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 809-834, September.

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