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Existence of a Solution and Variational Principles for Vector Equilibrium Problems

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  • Q. H. Ansari
  • I. V. Konnov
  • J. C. Yao

Abstract

In this paper, we prove an existence result for a solution to the vector equilibrium problems. Then, we establish variational principles, that is, vector optimization formulations of set-valued maps for vector equilibrium problems. A perturbation function

Suggested Citation

  • Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:3:d:10.1023_a:1017581009670
    DOI: 10.1023/A:1017581009670
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    References listed on IDEAS

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    1. I. V. Konnov, 2001. "Combined Relaxation Method for Monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 327-340, November.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    3. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    4. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
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    Cited by:

    1. Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    2. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    3. Yu Han & Nan-jing Huang, 2018. "Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 65-85, October.
    4. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    5. Szilárd László, 2016. "Vector Equilibrium Problems on Dense Sets," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 437-457, August.
    6. Bin Chen & Nan-jing Huang, 2013. "Continuity of the solution mapping to parametric generalized vector equilibrium problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1515-1528, August.
    7. Adela Capătă, 2011. "Existence results for proper efficient solutions of vector equilibrium problems and applications," Journal of Global Optimization, Springer, vol. 51(4), pages 657-675, December.
    8. Li, S.J. & Chen, C.R. & Wu, S.Y., 2009. "Conjugate dual problems in constrained set-valued optimization and applications," European Journal of Operational Research, Elsevier, vol. 196(1), pages 21-32, July.
    9. Chih-Sheng Chuang & Lai-Jiu Lin, 2013. "New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces," Journal of Global Optimization, Springer, vol. 57(2), pages 533-547, October.
    10. L. C. Ceng & G. Mastroeni & J. C. Yao, 2008. "Existence of Solutions and Variational Principles for Generalized Vector Systems," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 485-495, June.
    11. Chih-Sheng Chuang & Lai-Jiu Lin, 2013. "Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications," Journal of Global Optimization, Springer, vol. 57(3), pages 829-841, November.

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