Duality for an Extended Equilibrium Problem
Keywords:
Equilibrium problems, Fenchel duality, Lagrangian function, convex analysis.Abstract
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.
Downloads
Downloads
Published
Issue
Section
License
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
