IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v71y2023i5p1835-1856.html
   My bibliography  Save this article

Nonconvex Piecewise Linear Functions: Advanced Formulations and Simple Modeling Tools

Author

Listed:
  • Joey Huchette

    (Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005)

  • Juan Pablo Vielma

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for univariate functions using a geometric approach and for bivariate functions using a combinatorial approach. All formulations are strong, small (so-called logarithmic formulations), and have other desirable computational properties. We present extensive experiments in which they exhibit substantial computational performance improvements over existing approaches. To accompany these advanced formulations, we present PiecewiseLinearOpt , an extension of the JuMP modeling language in Julia that implements our models (alongside other formulations from the literature) through a high-level interface, hiding the complexity of the formulations from the end user.

Suggested Citation

  • Joey Huchette & Juan Pablo Vielma, 2023. "Nonconvex Piecewise Linear Functions: Advanced Formulations and Simple Modeling Tools," Operations Research, INFORMS, vol. 71(5), pages 1835-1856, September.
    • Handle: RePEc:inm:oropre:v:71:y:2023:i:5:p:1835-1856
    DOI: 10.1287/opre.2019.1973
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2019.1973
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2019.1973?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:71:y:2023:i:5:p:1835-1856. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.