Abstract
The paper is devoted to a new subdifferential version of Ekeland’s variational principle for set-valued maps in terms of Mordukhovich’s limiting differentiation, where Kuroiwa’s lower set-less preorder is used to compare images of set-valued maps. As a consequence, we study necessary conditions for strict positive minimizers of set-valued maps.
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Acknowledgements
This research was done during the visit of the authors to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, and it was support by a KFUPM funded research Project # IN171032. Authors are grateful to KFUPM for providing excellent research facilities during their visit to KFUPM. Authors are also grateful to the referees for their valuable comments and helpful suggestions, which have greatly improved this paper.
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Ansari, Q.H., Bao, T.Q. A limiting subdifferential version of Ekeland’s variational principle in set optimization. Optim Lett 15, 1537–1551 (2021). https://doi.org/10.1007/s11590-019-01489-8
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DOI: https://doi.org/10.1007/s11590-019-01489-8