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A dual view of equilibrium problems |
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| Authors: | Giancarlo Bigi Marco Castellani |
| Institution: | a Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy b Dipartimento di Sistemi e Istituzioni per l'Economia, Università di L'Aquila, Piazza del Santuario 19, 67040 Roio Poggio, L'Aquila, Italy c Universitatea Babe?-Bolyai Cluj-Napoca, Facultatea de Matematic? ?i Informatic?, Str. Mihail Kog?lniceanu nr. 1, RO-400084 Cluj-Napoca, Romania |
| Abstract: | The aim of this paper is to introduce and study a dual problem associated to a generalized equilibrium problem (GEP). We show that the solutions of (GEP) and its dual are strictly related to the saddle points of an associated Lagrangian function, and, under some suitable conditions, to the solutions of a family of parametric optimization problems and their dual problems. Our results allow us to show that well-known concepts and results from duality theory of some important particular cases of (GEP) like variational inequalities and optimization problems can be recovered. |
| Keywords: | Equilibrium problem Lagrangian function Dual equilibrium problem Fenchel duality |
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