Abstract
We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some set-equilibrium problems (whose formulations are inspired by set-optimization problems) and in the study of the existence of a solution of these problems we employ the generalized compactness investigated before. Several technical tools are needed throughout the presentation in order to fulfill these objectives. Furthermore, several illustrating examples are presented in order to clearly motivate our theoretical results.
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Acknowledgements
The authors thank Professor Constantin Zălinescu for some useful discussions and insights concerning the topic of Section 2.
Funding
This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P4-PCE-2021-0690, within PNCDI III.
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Communicated by Lionel Thibault.
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Durea, M., Florea, EA. Cone-Compactness of a Set and Applications to Set-Equilibrium Problems. J Optim Theory Appl 200, 1286–1308 (2024). https://doi.org/10.1007/s10957-024-02384-8
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DOI: https://doi.org/10.1007/s10957-024-02384-8