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

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  • E. E. A. Batista

    (IME, Universidade Federal de Goiás)

  • G. C. Bento

    (IME, Universidade Federal de Goiás)

  • O. P. Ferreira

    (IME, Universidade Federal de Goiás)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0761-5
    DOI: 10.1007/s10957-015-0761-5
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    References listed on IDEAS

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    1. Jun-Yi Fu & An-Hua Wan, 2002. "Generalized vector equilibrium problems with set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 259-268, November.
    2. Li-Wen Zhou & Nan-Jing Huang, 2013. "Existence of Solutions for Vector Optimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 44-53, April.
    3. Jun-Yi Fu, 2000. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 57-64, September.
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    Cited by:

    1. Glaydston de Carvalho Bento & João Xavier Cruz Neto & Ítalo Dowell Lira Melo, 2022. "Combinatorial Convexity in Hadamard Manifolds: Existence for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1087-1105, December.
    2. Glaydston C. Bento & João X. Cruz Neto & Jurandir O. Lopes & Ítalo D. L. Melo & Pedro Silva Filho, 2024. "A New Approach About Equilibrium Problems via Busemann Functions," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 428-436, January.
    3. 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.

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