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

Authors:
C. Gutiérrez;B. Jiménez;V. Novo
Affiliations:
Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Valladolid, Spain 47011;Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Madrid, Spain 28040;Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Madrid, Spain 28040
Venue:
Journal of Global Optimization
Year:
2011

Citing 11
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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.