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.

Bianchi, M., Pini, R. (2023). A Note on Fenchel Duality for Equilibrium Problems. MINIMAX THEORY AND ITS APPLICATIONS, 8(2), 409-422.

A Note on Fenchel Duality for Equilibrium Problems

Rita Pini
2023

Abstract

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.
Articolo in rivista - Articolo scientifico
Convex analysis; duality; equilibrium problems; Fenchel conjugation; robust solutions;
English
2023
8
2
409
422
reserved
Bianchi, M., Pini, R. (2023). A Note on Fenchel Duality for Equilibrium Problems. MINIMAX THEORY AND ITS APPLICATIONS, 8(2), 409-422.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/443318
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