Abstract
In this paper, we study characterizations and necessary conditions for nondominated points of sets and nondominated solutions of vector-valued functions in vector optimization with variable domination structure. We study not only the case, where the intersection of all the involved domination sets has a nonzero element, but also the case, where it might be the singleton. While the first case has been studied earlier, the second case has not, to the best of our knowledge, done yet. Our results extend and improve the existing results in vector optimization with a fixed ordering cone and with a variable ordering structure.
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Acknowledgements
The first author wishes to thank Department of Applied Mathematics for the very warm hospitality during his visit at Universidad Nacional de Educación a Distancia, Madrid and the Humboldt Foundation for financial support. This work, for the last three authors, was partially supported by the Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) (Spain) and Fondo Europeo de Desarrollo Regional (FEDER) under Project PGC2018-096899-B-I00 (MCIU/AEI/FEDER, UE), and also by ETSI Industriales, Universidad Nacional de Educación a Distancia (Spain) under Grant 2020-MAT09. The authors would like to thank the anonymous referees and the Editor for their helpful remarks, which allowed us to improve the original presentation.
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Communicated by Alfredo N. Iusem.
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Bao, T.Q., Huerga, L., Jiménez, B. et al. Necessary Conditions for Nondominated Solutions in Vector Optimization. J Optim Theory Appl 186, 826–842 (2020). https://doi.org/10.1007/s10957-020-01732-8
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DOI: https://doi.org/10.1007/s10957-020-01732-8
Keywords
- Vector optimization
- Domination structures
- Nondominated solutions
- Generalized differentiation
- Nonlinear scalarization functions