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A study of interval optimization problems

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Abstract

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.

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Acknowledgements

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).

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Tarapacá, Arica, Chile

    Iván Aguirre-Cipe, Rubén López, Exequiel Mallea-Zepeda & Lautaro Vásquez

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  1. Iván Aguirre-Cipe
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  2. Rubén López
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  3. Exequiel Mallea-Zepeda
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  4. Lautaro Vásquez
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Correspondence to Rubén López.

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The authors declare that they have no conflict of interest.

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This paper is dedicated to Professor Nicolas Hadjisavvas for the occasion of his 65th birthday.

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Aguirre-Cipe, I., López, R., Mallea-Zepeda, E. et al. A study of interval optimization problems. Optim Lett 15, 859–877 (2021). https://doi.org/10.1007/s11590-019-01496-9

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  • DOI: https://doi.org/10.1007/s11590-019-01496-9

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