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

Minty variational inequalities, increase-along-rays property and optimization

Contents:

Author Info

  • Crespi Giovanni P.

    ()
    (Facoltà di Scienze Economiche Aosta, Italy)

  • Ginchev Ivan

    ()
    (Department of Mathematics Varna, Bulgaria)

  • Rocca Matteo

    ()
    (Department of Economics, University of Insubria, Italy)

Registered author(s):

    Abstract

    Let E be a linear space, K E and f : K ? R. We put in terms of the lower Dini directional derivative a problem, referred to as GMV I(f ,K), which can be considered as a generalization of the Minty variational inequality of differential type (for short, MV I(f ,K)). We investigate, in the case of K star-shaped (for short, st-sh), the existence of a solution x of GMV I(f ,K) and the property of f to increase-along-rays starting at x (for short, f IAR(K, x )). We prove that GMV I(f ,K) with radially l.s.c. function f has a solution x ker K if and only if f IAR(K, x ). Further, we prove, that the solution set of GMV I(f ,K) is a convex and radially closed subset of kerK. We show also that, if GMV I(f ,K) has a solution x K, then x is a global minimizer of the problem f(x) ? min, x K. Moreover, we observe that the set of the global minimizers of the related optimization problem, its kernel, and the solution set of the variational inequality can be different. Finally, we prove, that in case of a quasi-convex function f, these sets coincide. Key words: Minty variational inequality, Generalized variational inequality, Existence of solutions, Increase along rays, Quasi-convex functions.

    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://eco.uninsubria.it/dipeco/Quaderni/files/QF2004_30.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf04019.

    as in new window
    Length: 21 pages
    Date of creation: Oct 2004
    Date of revision:
    Handle: RePEc:ins:quaeco:qf04019

    Contact details of provider:
    Postal: Via Ravasi 2-21100 Varese
    Web page: http://www.uninsubria.it/uninsubria/facolta/econo.html
    More information through EDIRC

    Related research

    Keywords:

    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:ins:quaeco:qf04019. 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: (Segreteria Dipartimento).

    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.