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A generic approach to approximate efficiency and applications to vector optimization with set-valued maps

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Abstract

In this paper we focus on approximate minimal points of a set in Hausdorff locally convex spaces. Our aim is to develop a general framework from which it is possible to deduce important properties of these points by applying simple results. For this purpose we introduce a new concept of ε-efficient point based on set-valued mappings and we obtain existence results and properties on the behavior of these approximate efficient points when ε is fixed and by considering that ε tends to zero. Finally, the obtained results are applied to vector optimization problems with set-valued mappings.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Paseo de Belén, 15, 47011, Valladolid, Spain

    C. Gutiérrez

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/Juan del Rosal, 12, 28040, Madrid, Spain

    B. Jiménez & V. Novo

Authors
  1. C. Gutiérrez
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  2. B. Jiménez
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  3. V. Novo
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Correspondence to C. Gutiérrez.

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Gutiérrez, C., Jiménez, B. & Novo, V. A generic approach to approximate efficiency and applications to vector optimization with set-valued maps. J Glob Optim 49, 313–342 (2011). https://doi.org/10.1007/s10898-010-9546-4

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  • DOI: https://doi.org/10.1007/s10898-010-9546-4

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