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An axiomatic approach to approximate solutions in vector optimization

  • 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)

Registered author(s):

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

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    1. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1998. "On consistent solutions for strategic games," Other publications TiSEM cc482511-a079-4067-88b2-0, Tilburg University, School of Economics and Management.
    2. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer, vol. 25(1), pages 13-34.
    3. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer, vol. 58(3), pages 375-385, December.
    4. Norde, H.W. & Patrone, F. & Tijs, S.H., 1996. "Characterizing properties of approximate solutions for optimization problems," Discussion Paper 1996-101, Tilburg University, Center for Economic Research.
    5. repec:spr:compst:v:58:y:2003:i:3:p:375-385 is not listed on IDEAS
    6. 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.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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