A Formula for the Set of Optimal Solutions of a Relaxed Minimization Problem. Applications to Subdifferential Calculus

Marco A. López; Michel Volle

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Relaxed minimization problem
approximate minima
epsilon-subdifferential calculus
Legendre-Fenchel conjugate

Mathematics Subject Classification

90C48, 90C46; 49N15, 90C25

Suggested citation

M. A. López, M. Volle. “A Formula for the Set of Optimal Solutions of a Relaxed Minimization Problem. Applications to Subdifferential Calculus.” Journal of Convex Analysis 17 (2010), No. 3&4, 1057–1075.