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Scalar characterization of explicitly quasiconvex set-valued maps

Author

Listed:
  • Davide LA TORRE
  • Nicolae POPOVICI
  • Matteo ROCCA

Abstract

This paper concerns explicitly quasiconvex set-valued maps,defined on a nonempty convex subset of a real linear space with values in a partially ordered real linear space, with respect to a solid vectorially closed convex cone. It is shown that these generalized convex set-valued maps can be characterized in terms of classical explicit quasiconvexity of certain scalar functions.

Suggested Citation

  • Davide LA TORRE & Nicolae POPOVICI & Matteo ROCCA, 2008. "Scalar characterization of explicitly quasiconvex set-valued maps," Departmental Working Papers 2008-01, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2008-01
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    File URL: http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_001wp.pdf
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    References listed on IDEAS

    as
    1. Joël Benoist & Nicolae Popovici, 2003. "Characterizations of convex and quasiconvex set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 427-435, August.
    2. A. Daniilidis & N. Hadjisavvas & S. Schaible, 1997. "Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 517-524, June.
    3. Adan, M. & Novo, V., 2003. "Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness," European Journal of Operational Research, Elsevier, vol. 149(3), pages 641-653, September.
    4. Davide Torre, 2007. "On Arcwise Connected Convex Multifunctions," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 337-345, Springer.
    5. J. Benoist, 2001. "Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 325-336, August.
    Full references (including those not matched with items on IDEAS)

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