Journal of Convex Analysis 17 (2010), No. 3&4, 1057--1075
Copyright Heldermann Verlag 2010
A Formula for the Set of Optimal Solutions of a Relaxed Minimization Problem. Applications to Subdifferential Calculus
Marco A. López
Dept. of Statistics and Operations Research, University of Alicante, Apt. de Correos 99, 03080 Alicante, Spain
marco.antonio@ua.es
Michel Volle
Université d'Avignon et des Pays de Vaucluse, 74 Rue Louis Pasteur, 84029 Avignon, France
Michel.Volle@univ-avignon.fr
In the infinite dimensional setting, we provide a general formula for the optimal set of a relaxed minimization problem in terms of the approximate minima of the data function. Various applications to the ε-subdifferential calculus are also given.
Keywords: Relaxed minimization problem, approximate minima, epsilon-subdifferential calculus, Legendre-Fenchel conjugate.
MSC: 90C48, 90C46; 49N15, 90C25
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