A Generalized Variational Principle and Its Application to Equilibrium Problems

Csaba Farkas () and Andrea Éva Molnár ()
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Csaba Farkas: Babeş-Bolyai University
Andrea Éva Molnár: Babeş-Bolyai University

Journal of Optimization Theory and Applications, 2013, vol. 156, issue 2, No 2, 213-231

Abstract: 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.

Keywords: Equilibrium problem; System of equilibrium problems; Approximate solution; Ekeland-type variational principles; Zhong type variational principles (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0101-y

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