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Scalar characterization of explicitly quasiconvex set-valued maps


  • Davide LA TORRE


  • Nicolae POPOVICI


  • Matteo ROCCA



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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    References listed on IDEAS

    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. repec:spr:compst:v:57:y:2003:i:3:p:427-435 is not listed on IDEAS
    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.
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    Explicitly quasiconvex set-valued maps; ordered linear spaces; strictly monotonic functionals; scalarization;

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