A study of interval optimization problems

  • Iván Aguirre-Cipe
  • Rubén LópezEmail author
  • Exequiel Mallea-Zepeda
  • Lautaro Vásquez
Original Paper


We study optimization problems with interval objective functions. We focus on set-type solution notions defined using the Kulisch–Miranker order between intervals. We obtain bounds for the asymptotic cones of level, colevel and solution sets that allow us to deduce coercivity properties and coercive existence results. Finally, we obtain various noncoercive existence results. Our results are easy to check since they are given in terms of the asymptotic cone of the constraint set and the asymptotic functions of the end point functions. This work extends, unifies and sheds new light on the theory of these problems.


Asymptotic cones Asymptotic functions Coercivity properties Coercive and noncoercive existence results Set-type solutions Interval optimization problems 



The authors want to express their gratitude to the editor and referees for their criticism and suggestions that helped to improve the paper. This work was supported by Universidad de Tarapacá [project UTA-Mayor 4731-13] (Vásquez) and Conicyt-Gobierno de Chile [project Fondecyt 1181368] (López).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad de TarapacáAricaChile

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