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Generalized \({\varepsilon }\)-quasi solutions of set optimization problems

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Abstract

We introduce notions of generalized \(\varepsilon \)-quasi solutions to approximate set type solutions of set optimization problems. We study their properties, consistency and limit behavior as approximations to efficient and strict weak efficient solutions. Moreover, we prove an existence result for such solutions and a bound for their asymptotic cone. Finally, we obtain optimality conditions for them.

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Acknowledgements

The authors are very grateful to the anonymous referee for his/her helpful comments and suggestions. This work has been partially supported by projects: PID2020-112491GB-I00 / AEI / 10.13039/501100011033 through the Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación, Spain (Gutiérrez, López), Fondecyt 1181368 through ANID-Chile (López, Martínez) and Apoyo Institucional para el Magíster Académico de la Universidad de Tarapacá, Chile (Martínez).

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Authors and Affiliations

  1. Mathematics Research Institute (IMUVA), University of Valladolid, Paseo de Belén S/N, Campus Miguel Delibes, 47011, Valladolid, Spain

    C. Gutiérrez

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

    R. López & J. Martínez

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  1. C. Gutiérrez
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  2. R. López
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  3. J. Martínez
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Correspondence to R. López.

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Gutiérrez, C., López, R. & Martínez, J. Generalized \({\varepsilon }\)-quasi solutions of set optimization problems. J Glob Optim 82, 559–576 (2022). https://doi.org/10.1007/s10898-021-01098-9

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  • DOI: https://doi.org/10.1007/s10898-021-01098-9

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