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About Asymptotic Analysis and Set Optimization

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Abstract

We introduce, in a natural way, a new notion of asymptotic map for a set-valued map. The non-uniqueness of such an asymptotic map leads to consider equivalent classes via a set relation. We provide fundamental analytic representations and computational formulae for the asymptotic map. Asymptotic tools for studying set optimization problems have been developed. As applications, new coercivity notions and existence results for set optimization problems with unbounded constraint sets are obtained.

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Acknowledgements

This research was partially supported by project ETSI Industriales (UNED) 2018-MAT10 (Hernández) and by project Fondecyt Regular 1150440 (López). We would like to thank the anonymous referees for their helpful suggestions and comments on an earlier version of this paper.

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Authors and Affiliations

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

    Elvira Hernández

  2. Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá, Avenida 18 de Septiembre 2222, Campus Saucache, Casilla 7B, Arica, Chile

    Rubén López

Authors
  1. Elvira Hernández
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  2. Rubén López
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Correspondence to Elvira Hernández.

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Hernández, E., López, R. About Asymptotic Analysis and Set Optimization. Set-Valued Var. Anal 27, 643–664 (2019). https://doi.org/10.1007/s11228-018-0468-5

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  • DOI: https://doi.org/10.1007/s11228-018-0468-5

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