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On the Derivation of Continuous Piecewise Linear Approximating Functions

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  • Lingxun Kong

    (Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706)

  • Christos T. Maravelias

    (Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706)

Abstract

We propose mixed-integer programming models for fitting univariate discrete data points with continuous piecewise linear (PWL) functions. The number of approximating function segments and the locations of break points are optimized simultaneously. The proposed models include linear constraints and convex objective function and, thus, are computationally more efficient than previously proposed mixed-integer nonlinear programming models. We also show how the proposed models can be extended to approximate univariate functions with PWL functions with the minimum number of segments subject to bounds on the pointwise error.

Suggested Citation

  • Lingxun Kong & Christos T. Maravelias, 2020. "On the Derivation of Continuous Piecewise Linear Approximating Functions," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 531-546, July.
    • Handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:531-546
    DOI: 10.1287/ijoc.2019.0949
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    References listed on IDEAS

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    1. Toriello, Alejandro & Vielma, Juan Pablo, 2012. "Fitting piecewise linear continuous functions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 86-95.
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    5. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, INFORMS, vol. 58(2), pages 303-315, April.
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    Cited by:

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    3. Mohammadi Fathabad, Abolhassan & Cheng, Jianqiang & Pan, Kai & Yang, Boshi, 2023. "Asymptotically tight conic approximations for chance-constrained AC optimal power flow," European Journal of Operational Research, Elsevier, vol. 305(2), pages 738-753.
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    5. John Alasdair Warwicker & Steffen Rebennack, 2022. "A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1042-1047, March.
    6. Ploussard, Quentin, 2024. "Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation," European Journal of Operational Research, Elsevier, vol. 315(1), pages 50-62.

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