IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Decomposition and Nondifferentiable Optimization with the Projective Algorithm

  • J. L. Goffin

    (GERAD, Faculty of Management, McGill University, Montreal, Quebec, Canada H3A 1G5)

  • A. Haurie

    (GERAD, Ecole des Hautes Etudes Commerciales de Montreal, Montreal, Quebec, Canada and Departement d'Economie Commerciale et Industrielle, Université de Genève, Geneva, Switzerland)

  • J. P. Vial

    (Departement d'Economie Commerciale et Industrielle, Université de Genève, Geneva, Switzerland)

Registered author(s):

    This paper deals with an application of a variant of Karmarkar's projective algorithm for linear programming to the solution of a generic nondifferentiable minimization problem. This problem is closely related to the Dantzig-Wolfe decomposition technique used in large-scale convex programming. The proposed method is based on a column generation technique defining a sequence of primal linear programming maximization problems. Associated with each problem one defines a weighted potential function which is minimized using a variant of the projective algorithm. When a point close to the minimum of the potential function is reached, a corresponding point in the dual space is constructed, which is close to the analytic center of a polytope containing the solution set of the nondifferentiable optimization problem. An admissible cut of the polytope, corresponding to a new supporting hyperplane of the epigraph of the function to minimize, is then generated at this approximate analytic center. In the primal space this new cut translates into a new column for the associated linear programming problem. The algorithm has performed well on a set of convex nondifferentiable programming problems.

    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://dx.doi.org/10.1287/mnsc.38.2.284
    Download Restriction: no

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 2 (February)
    Pages: 284-302

    as
    in new window

    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:2:p:284-302
    Contact details of provider: Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA
    Phone: +1-443-757-3500
    Fax: 443-757-3515
    Web page: http://www.informs.org/Email:


    More information through EDIRC

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

    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:inm:ormnsc:v:38:y:1992:i:2:p:284-302. 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: (Mirko Janc)

    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.