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

Partitioning Procedure for Polynomial Optimization: Application to Portfolio Decisions with Higher Order Moments

Contents:

Author Info

  • P. M. Kleniati
  • Panos Parpas
  • Berc Rustem
Registered author(s):

    Abstract

    We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition. Towards this goal we introduce a partitioning procedure. The problem manipulations are in line with the pattern used in the Benders decomposition [1], namely relaxation preceded by projection. Stengle’s and Putinar’s Positivstellensatz are employed to derive the so-called feasibility and optimality constraints, respectively. We test the performance of the proposed method on a collection of benchmark problems and we present the numerical results. As an application, we consider the problem of selecting an investment portfolio optimizing the mean, variance, skewness and kurtosis of the portfolio.

    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://comisef.eu/files/wps023.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by COMISEF in its series Working Papers with number 023.

    as in new window
    Length: 30 pages
    Date of creation: 10 Nov 2009
    Date of revision:
    Handle: RePEc:com:wpaper:023

    Contact details of provider:
    Web page: http://www.comisef.eu

    Related research

    Keywords: Polynomial optimization; Semidefinite relaxations; Positivstellensatz; Sum of squares; Benders decomposition; Portfolio optimization;

    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:com:wpaper:023. 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: (Anil Khuman).

    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.