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On maximal monotonicity of bifunctions on Hadamard manifolds

Author

Listed:
  • J. X. Cruz Neto

    (Universidade Federal do Piauí)

  • F. M. O. Jacinto

    (Universidade Federal do Amazonas)

  • P. A. Soares

    (Universidade Estadual do Piauí)

  • J. C. O. Souza

    (Universidade Federal do Piauí)

Abstract

We study some conditions for a monotone bifunction to be maximally monotone by using a corresponding vector field associated to the bifunction and vice versa. This approach allows us to establish existence of solutions to equilibrium problems in Hadamard manifolds obtained by perturbing the equilibrium bifunction.

Suggested Citation

  • J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:3:d:10.1007_s10898-018-0663-9
    DOI: 10.1007/s10898-018-0663-9
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    References listed on IDEAS

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    1. E. E. A. Batista & G. C. Bento & O. P. Ferreira, 2015. "An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 550-557, November.
    2. O. P. Ferreira & P. R. Oliveira, 1998. "Subgradient Algorithm on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 93-104, April.
    3. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    4. J. H. Wang & G. López & V. Martín-Márquez & C. Li, 2010. "Monotone and Accretive Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 691-708, September.
    5. I.V. Konnov, 2003. "Application of the Proximal Point Method to Nonmonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 317-333, November.
    6. Mohammad Alizadeh & Nicolas Hadjisavvas, 2012. "Local boundedness of monotone bifunctions," Journal of Global Optimization, Springer, vol. 53(2), pages 231-241, June.
    7. Abdellatif Moudafi, 2010. "Proximal methods for a class of bilevel monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 287-292, June.
    8. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, January.
    9. M. Alizadeh & M. Bianchi & N. Hadjisavvas & R. Pini, 2014. "On cyclic and $$n$$ n -cyclic monotonicity of bifunctions," Journal of Global Optimization, Springer, vol. 60(4), pages 599-616, December.
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    Cited by:

    1. G. C. Bento & J. X. Cruz Neto & P. A. Soares & A. Soubeyran, 2022. "A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires," Annals of Operations Research, Springer, vol. 316(2), pages 1301-1318, September.

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