Abstract
We present a sufficient condition for the existence of a solution to the generalized vector equilibrium problem on Hadamard manifolds using a version of the Knaster–Kuratowski–Mazurkiewicz Lemma. In particular, the existence of solutions to optimization, vector optimization, Nash equilibria, complementarity, and variational inequality problems is a special case of the existence result for the generalized vector equilibrium problem.
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Acknowledgments
The work was supported by CAPES, CAPES-MES-CUBA 226/2012, FAPEG 201210267000909-05/2012 and CNPq Grants 458479/2014-4, 471815/2012-8, 303732/2011-3.
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Communicated by Sándor Zoltán Németh.
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Batista, E.E.A., Bento, G.C. & Ferreira, O.P. An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds. J Optim Theory Appl 167, 550–557 (2015). https://doi.org/10.1007/s10957-015-0761-5
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DOI: https://doi.org/10.1007/s10957-015-0761-5