Advanced Search
MyIDEAS: Login to save this paper or follow this series

Extensions of the CQ Algorithm for the Split Feasibility and Split Equality Problems

Contents:

Author Info

  • Charles L. Byrne and Abdellatif Moudafi

    ()
    (Department of Mathematical Sciences, University of Massachusetts
    Ceregmia-Département Scientifique Interfacultaire)

Registered author(s):

    Abstract

    The convex feasibility problem (CFP) is to find a member of the intersection of finitely many closed convex sets in Euclidean space. When the intersection is empty, one can minimize a proximity function to obtain an approximate solution to the problem. The split feasibility problem (SFP) and the split equality problem (SEP) are generalizations of the CFP. The approximate SFP (ASFP) and approximate SEP (ASEP) involve finding only approximate solutions to the SFP and SEP, respectively. We present here the SSEA, a simultaneous iterative algorithm for solving the ASEP. When this algorithm is applied to the ASFP it resembles closely, but is not equivalent to, the CQ algorithm. The SSEA involves orthogonal projection onto the given closed convex sets. The relaxed SSEA (RSSEA) is an easily implementable variant of the SSEA that uses orthogonal projection onto half-spaces at each step to solve the SEP. The perturbed version of the SSEA (PSSEA) is similar to the RSSEA, but uses orthogonal projection onto a sequence of epi-convergent closed convex sets.

    Download Info

    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://www2.univ-ag.fr/RePEc/DT/DT2013-01_Byrne_Moudafi.pdf
    File Function: First version, 2012
    Download Restriction: no

    Bibliographic Info

    Paper provided by CEREGMIA, Université des Antilles et de la Guyane in its series Documents de Travail with number 2013-01.

    as in new window
    Length: 15 pages
    Date of creation: Jan 2013
    Date of revision:
    Handle: RePEc:crg:wpaper:dt2013-01

    Contact details of provider:
    Postal: Campus de Schoelcher, B.P. 7209, 97275 Schoelcher Cedex
    Phone: 05.96.72.74.00
    Fax: 05.96.72.74.03
    Email:
    Web page: http://www.ceregmia.eu/
    More information through EDIRC

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Lists

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

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:crg:wpaper:dt2013-01. 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: (Janis Hilaricus).

    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.