Journal of Optimization Theory and Applications

, Volume 167, Issue 2, pp 550–557 | Cite as

An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds

  • E. E. A. Batista
  • G. C. Bento
  • O. P. Ferreira


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.


Vector equilibrium problem Vector optimization Hadamard manifold 

AMS subject classification

90C33 65K05 47J25 91E10 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • E. E. A. Batista
    • 1
  • G. C. Bento
    • 1
  • O. P. Ferreira
    • 1
  1. 1.IME, Universidade Federal de GoiásGoiâniaBR

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