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On Equilibrium Problems

In: Optimization and Optimal Control

Author

Listed:
  • Gábor Kassay

    (Babes-Bolyai University)

Abstract

Summary In this chapter we give an overview of the theory of scalar equilibrium problems. To emphasize the importance of this problem in nonlinear analysis and in several applied fields we first present its most important particular cases as optimization, Kirszbraun’s problem, saddlepoint (minimax) problems, and variational inequalities. Then, some classical and new results together with their proofs concerning existence of solutions of equilibrium problems are exposed. The existence of approximate solutions via Ekeland’s variational principle – extended to equilibrium problems – is treated within the last part of the chapter.

Suggested Citation

  • Gábor Kassay, 2010. "On Equilibrium Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 55-83, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-89496-6_3
    DOI: 10.1007/978-0-387-89496-6_3
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    Citations

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    Cited by:

    1. Adela Capătă, 2012. "Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 661-674, March.
    2. Mircea Balaj & Dan Florin Serac, 2023. "Generalized Equilibrium Problems," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    3. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    4. Boualem Alleche & Vicenţiu D. Rădulescu, 2016. "Solutions and Approximate Solutions of Quasi-Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 629-649, August.
    5. Mohammad Alizadeh & Nicolas Hadjisavvas, 2012. "Local boundedness of monotone bifunctions," Journal of Global Optimization, Springer, vol. 53(2), pages 231-241, June.
    6. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    7. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Well-posedness for the optimistic counterpart of uncertain vector optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 517-533, December.

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