IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v58y2014i1p249-272.html
   My bibliography  Save this article

Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions

Author

Listed:
  • Bryan Gardiner
  • Khan Jakee
  • Yves Lucet

Abstract

Piecewise linear-quadratic (PLQ) functions are an important class of functions in convex analysis since the result of most convex operators applied to a PLQ function is a PLQ function. We modify a recent algorithm for computing the convex (Legendre-Fenchel) conjugate of convex PLQ functions of two variables, to compute its partial conjugate i.e. the conjugate with respect to one of the variables. The structure of the original algorithm is preserved including its time complexity (linear time with some approximation and log-linear time without approximation). Applying twice the partial conjugate (and a variable switching operator) recovers the full conjugate. We present our partial conjugate algorithm, which is more flexible and simpler than the original full conjugate algorithm. We emphasize the difference with the full conjugate algorithm and illustrate results by computing partial conjugates, partial Moreau envelopes, and partial proximal averages. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:1:p:249-272
    DOI: 10.1007/s10589-013-9622-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-013-9622-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-013-9622-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bryan Gardiner & Yves Lucet, 2011. "Graph-Matrix Calculus for Computational Convex Analysis," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 243-259, Springer.
    2. Heinz H. Bauschke & Sarah M. Moffat & Xianfu Wang, 2011. "Self-Dual Smooth Approximations of Convex Functions via the Proximal Average," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 23-32, Springer.
    3. 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.
    4. Jennifer A. Johnstone & Valentin R. Koch & Yves Lucet, 2011. "Convexity of the Proximal Average," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 107-124, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tasnuva Haque & Yves Lucet, 2018. "A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 70(2), pages 593-613, June.
    2. Anuj Bajaj & Warren Hare & Yves Lucet, 2017. "Visualization of the $$\varepsilon $$ ε -subdifferential of piecewise linear–quadratic functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 421-442, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jennifer A. Johnstone & Valentin R. Koch & Yves Lucet, 2011. "Convexity of the Proximal Average," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 107-124, January.
    2. Tasnuva Haque & Yves Lucet, 2018. "A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 70(2), pages 593-613, June.
    3. Anuj Bajaj & Warren Hare & Yves Lucet, 2017. "Visualization of the $$\varepsilon $$ ε -subdifferential of piecewise linear–quadratic functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 421-442, June.

    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:spr:coopap:v:58:y:2014:i:1:p:249-272. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.