A generic approach to approximate efficiency and applications to vector optimization with set-valued maps |
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Authors: | C Gutiérrez B Jiménez V Novo |
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Institution: | 1.Departamento de Matemática Aplicada, E.T.S.I. Informática,Universidad de Valladolid,Valladolid,Spain;2.Departamento de Matemática Aplicada, E.T.S.I. Industriales,Universidad Nacional de Educación a Distancia,Madrid,Spain |
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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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