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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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