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Minimax Theory and its Applications 03 (2018), No. 1, 091--106
Copyright Heldermann Verlag 2018

Duality for an extended equilibrium problem

Liana Timbos
Faculty of Automation and Computer Science, Technical University, 26-28 G. Baritiu, 400027 Cluj Napoca, Romania

We consider an extended equilibrium problem with sum of two functions, one being composed with a linear mapping and we introduce and study a dual problem associated to it. We show that the solutions of the two problems are strictly related to the saddle points of an associated Lagrangian function and, under appropriate conditions, to the solutions of the associated optimization problem and its dual. Among the special instances of our results, we rediscover results obtained for the generalized equilibrium problem considered by Bigi, Castellani and Kassay, and we also prove that for some particular cases the duality scheme considered here become the duality scheme concerning variational inequalities introduced in the literature.

Keywords: Equilibrium problems, Fenchel duality, Lagrangian function, convex analysis.

MSC: 90C33, 49N15, 46A20, 90C25

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