Duality for generalized equilibrium problem

Authors: Jacinto, Flavia Morgana¹; Scheimberg, Susana²

Source: Optimization, Volume 57, Number 6, January 2008 , pp. 795-805(11)

Publisher: Taylor and Francis Ltd

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Abstract:

We introduce a generalized equilibrium problem (GEP) that allow us to develop a robust dual scheme for this problem, based on the theory of conjugate functions. We obtain a unified dual analysis for interesting problems. Indeed, the Lagrangian duality for convex optimization is a particular case of our dual problem. We establish necessary and sufficient optimality conditions for GEP that become a well-known theorem given by Mosco and the dual results obtained by Morgan and Romaniello, which extend those introduced by Auslender and Teboulle for a variational inequality problem.

Keywords: equilibrium problems; duality analysis; conjugate functions

Document Type: Research article

DOI: 10.1080/02331930701761458

Affiliations: 1: Depto. de Matematica, ICE-UFAM, Manaus, Brazil 2: IM, PESC/COPPE-UFRJ, Rio de Janeiro, Brazil

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