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Benson Proper Efficiency in Set-Valued Optimization on Real Linear Spaces

In: Recent Advances in Optimization

Author

Listed:
  • Elvira Hernández

    (Departamento de Matemática Aplicada)

  • Bienvenido Jiménez

    (Universidad de Salamanca, Facultad de Economía y Empresa)

  • Vicente Novo

    (Departamento de Matemática Aplicada)

Abstract

Summary In this work, a notion of cone-subconvexlikeness of set-valued maps on linear spaces is given and several characterizations are obtained. An alternative theorem is also established for this kind of set-valued maps. Using the notion of vector closure introduced recently by Adán and Novo, we also provide, in this framework, an adaptation of the proper efficiency in the sense of Benson for set-valued maps. The previous results are then applied to obtain different optimality conditions for this Benson-vectorial proper efficiency by using scalarization and multiplier rules.

Suggested Citation

  • Elvira Hernández & Bienvenido Jiménez & Vicente Novo, 2006. "Benson Proper Efficiency in Set-Valued Optimization on Real Linear Spaces," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 45-59, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_4
    DOI: 10.1007/3-540-28258-0_4
    as

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