Geodesic
A Note on Fenchel Duality for Equilibrium Problems
Minimax theory and its applications, Tome 8 (2023) no. 2
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By means of the Fenchel duality, we introduce a dual problem associated to an equilibrium problem that turns out to be an equilibrium problem itself in the dual space. We present conditions which entail the solvability of the primal and dual problem. Moreover, we introduce the notion of robust and optimistic solution for parametric equilibrium problems, and we show that the solutions of the dual of the robust problem coincide with the optimistic solutions of the dual parametric equilibrium problem.
Mots-clés : Convex analysis, duality, equilibrium problems, Fenchel conjugation, robust solutions 
@article{MTA_2023_8_2_a7,
     author = {Monica Bianchi,Rita Pini},
     title = {A {Note} on {Fenchel} {Duality} for {Equilibrium} {Problems}},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a7/}
}
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Monica Bianchi,Rita Pini. A Note on Fenchel Duality for Equilibrium Problems. Minimax theory and its applications, Tome 8 (2023) no. 2. http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a7/