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Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions

Author

Listed:
  • Jon Lee

    (University of Michigan)

  • Daphne Skipper

    (United States Naval Academy)

  • Emily Speakman

    (University of Colorado)

  • Luze Xu

    (University of Michigan)

Abstract

We study mixed-integer nonlinear optimization (MINLO) formulations of the disjunction $$x\in \{0\}\cup [\ell ,u]$$ x ∈ { 0 } ∪ [ ℓ , u ] , where z is a binary indicator for $$x\in [\ell ,u]$$ x ∈ [ ℓ , u ] ( $$0 \le \ell 1$$ p > 1 .

Suggested Citation

  • Jon Lee & Daphne Skipper & Emily Speakman & Luze Xu, 2023. "Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 1-35, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02144-6
    DOI: 10.1007/s10957-022-02144-6
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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. 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.
    3. J. Berenguel & L. Casado & I. García & E. Hendrix & F. Messine, 2013. "On interval branch-and-bound for additively separable functions with common variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1101-1121, July.
    4. Hassan Hijazi & Pierre Bonami & Adam Ouorou, 2014. "An Outer-Inner Approximation for Separable Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 31-44, February.
    5. Jon Lee & Daphne Skipper & Emily Speakman, 2022. "Gaining or losing perspective," Journal of Global Optimization, Springer, vol. 82(4), pages 835-862, April.
    6. LEE, Jon & WILSON, Dan, 2001. "Polyhedral methods for piecewise-linear functions I: the lambda method," LIDAM Reprints CORE 1493, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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