Abstract
In this paper, we prove a generalized Ekeland-type variational principle for bifunctions, by showing the existence of solution for some generalized optimization problems. In a particular case, from this result, we obtain a Zhong-type variational principle for bifunctions, which may be important from algorithmic point of view, because the solution can be localized in a sphere. Contrary to the standard literature, we are able to guarantee the existence of solution without assuming the triangle property.
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Acknowledgements
The authors would like to thank Professor Csaba Varga and to Professor Alexandru Kristály for their helpful comments concerning this paper. The author Andrea Éva Molnár has been supported by Project POSDRU/CPP107/DMI1.5/S/76841 “Modern Doctoral Studies: Internationalization and Interdisciplinarity”/“Studii doctorale moderne: internaţionalizare şi interdisciplinaritate” (Project co-financed by the Sectoral Operational Program For Human Resources Development 2007–2013, Babe’s-Bolyai University, Cluj-Napoca, Romania).
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Communicated by Suliman Saleh Al-Homidan.
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Farkas, C., Molnár, A.É. A Generalized Variational Principle and Its Application to Equilibrium Problems. J Optim Theory Appl 156, 213–231 (2013). https://doi.org/10.1007/s10957-012-0101-y
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DOI: https://doi.org/10.1007/s10957-012-0101-y