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On Weak Multifunction Equilibrium Problems

In: Variational Analysis and Generalized Differentiation in Optimization and Control

Author

Listed:
  • Adela Capătă

    (Technical University of Cluj-Napoca)

  • Gábor Kassay

    (Babeş-Bolyai University)

  • Boglárka Mosoni

    (Babeş-Bolyai University)

Abstract

This chapter deals with an extended form of the scalar equilibrium problem called the weak multifunction equilibrium problem. New existence results are obtained in the general setting using a well-known separation theorem in infinite dimensional spaces. These results are applied for the particular case of real-valued multifunctions. Furthermore, two gap functions associated with the studied problems are constructed, where, for one of them, the Fenchel duality theory of optimization is used.

Suggested Citation

  • Adela Capătă & Gábor Kassay & Boglárka Mosoni, 2010. "On Weak Multifunction Equilibrium Problems," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 133-148, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0437-9_6
    DOI: 10.1007/978-1-4419-0437-9_6
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