Abstract
The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin–Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.
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Acknowledgements
The authors wish to thank the Editors and anonymous Referees for their helpful remarks and suggestions that helped us significantly improve the paper. The second author is supported by the Institute for Computational Science and Technology (ICST) under the grant number 03/2019/HD-KHCNTT.
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Anh, L.Q., Duy, T.Q. & Khanh, P.Q. Levitin–Polyak well-posedness for equilibrium problems with the lexicographic order. Positivity 25, 1323–1349 (2021). https://doi.org/10.1007/s11117-021-00818-5
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DOI: https://doi.org/10.1007/s11117-021-00818-5
Keywords
- Lexicographic equilibrium problem
- Optimization problem with lexicographic equilibrium constraints
- Levitin–Polyak well-posedness
- Potential game
- Nontransitive consumer