IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Visualization of the $$\varepsilon $$ ε -subdifferential of piecewise linear–quadratic functions

Listed author(s):
  • Anuj Bajaj

    ()

    (Wayne State University)

  • Warren Hare

    ()

    (The University of British Columbia - Okanagan (UBCO))

  • Yves Lucet

    ()

    (The University of British Columbia - Okanagan (UBCO))

Registered author(s):

    Abstract Computing explicitly the $$\varepsilon $$ ε -subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear–quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted–Rockafellar theorem.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://link.springer.com/10.1007/s10589-017-9892-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 67 (2017)
    Issue (Month): 2 (June)
    Pages: 421-442

    as
    in new window

    Handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9892-y
    DOI: 10.1007/s10589-017-9892-y
    Contact details of provider: Web page: http://www.springer.com

    Order Information: Web: http://www.springer.com/math/journal/10589

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as
    in new window


    1. Bryan Gardiner & Khan Jakee & Yves Lucet, 2014. "Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 58(1), pages 249-272, May.
    2. Yves Lucet & Heinz Bauschke & Mike Trienis, 2009. "The piecewise linear-quadratic model for computational convex analysis," Computational Optimization and Applications, Springer, vol. 43(1), pages 95-118, May.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9892-y. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)

    or (Rebekah McClure)

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.