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Well-posedness for vector equilibrium problems

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Abstract

We introduce and study two notions of well-posedness for vector equilibrium problems in topological vector spaces; they arise from the well-posedness concepts previously introduced by the same authors in the scalar case, and provide an extension of similar definitions for vector optimization problems. The first notion is linked to the behaviour of suitable maximizing sequences, while the second one is defined in terms of Hausdorff convergence of the map of approximate solutions. In this paper we compare them, and, in a concave setting, we give sufficient conditions on the data in order to guarantee well-posedness. Our results extend similar results established for vector optimization problems known in the literature.

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Authors and Affiliations

  1. Università Cattolica del Sacro Cuore di Milano, Milan, Italy

    M. Bianchi

  2. Babes-Bolyai University Cluj, Cluj-Napoca, Romania

    G. Kassay

  3. Università degli Studi di Milano Bicocca, Milan, Italy

    R. Pini

Authors
  1. M. Bianchi
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  2. G. Kassay
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  3. R. Pini
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Correspondence to R. Pini.

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Bianchi, M., Kassay, G. & Pini, R. Well-posedness for vector equilibrium problems. Math Meth Oper Res 70, 171–182 (2009). https://doi.org/10.1007/s00186-008-0239-4

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  • DOI: https://doi.org/10.1007/s00186-008-0239-4

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