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An axiomatic approach to approximate solutions in vector optimization

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Author Info

  • Miglierina Enrico

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

  • Molho Elena

    ()
    (Department of Management Sciences, University of Pavia)

  • Patrone Fioravante

    ()
    (Department of Mathematics, University of Genoa, Italy)

  • Steff H. Tijs

    ()
    (Department of Econometrics, University of Tilburg, Netherlands)

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    Abstract

    In vector optimization many notions of approximate solution have been proposed in the literature. In this paper an axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. An impossibility result is proved in the sense that, whenever all of the axioms are satisfied, either the set of the approximate solutions is a subset of the exact solution of the problem (the weakly efficient frontier), or it coincides with the whole admissible set. Moreover, the geometry of the approximate solution map is studied in the special case of polyhedral ordering cones generated by a base of R. Finally, we study the shape of the approximate solution map under the assumption of weak approximation consistency.

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    File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2005_10.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0507.

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    Length: 30 pages
    Date of creation: Sep 2005
    Date of revision:
    Handle: RePEc:ins:quaeco:qf0507

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    Related research

    Keywords: vector optimization; approximate solution; axiomatization.;

    This paper has been announced in the following NEP Reports:

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    1. Peleg, B. & Tijs, S.H., 1993. "The consistency principle for games in strategic form," Discussion Paper 1993-6, Tilburg University, Center for Economic Research.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Norde, H.W. & Patrone, F. & Tijs, S.H., 2000. "Characterizing properties of approximate solutions for optimization problems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-84117, Tilburg University.
    4. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Computational Statistics, Springer, vol. 58(3), pages 375-385, December.
    5. Graziano Pieri & Fioravante Patrone & Anna Torre & Stef Tijs, 1998. "On consistent solutions for strategic games," International Journal of Game Theory, Springer, vol. 27(2), pages 191-200.
    6. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1998. "On consistent solutions for strategic games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-77113, Tilburg University.
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