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Optimization and Optimal Control pp 55–83Cite as

On Equilibrium Problems

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 39))

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.

Work supported by the grant PNII, ID 523/2007

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj, Romania

    Gábor Kassay

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  1. Gábor Kassay
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Correspondence to Gábor Kassay .

Editor information

Editors and Affiliations

  1. South Kensington Campus, London, SW7 2AZ, United Kingdom

    Altannar Chinchuluun

  2. Dept. Industrial & Systems, Engineering, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. Labo. PRISM, Université Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Ider Tseveendorj

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Kassay, G. (2010). On Equilibrium Problems. In: Chinchuluun, ., Pardalos, P., Enkhbat, R., Tseveendorj, I. (eds) Optimization and Optimal Control. Springer Optimization and Its Applications(), vol 39. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89496-6_3

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