
Journal of Convex Analysis 23 (2016), No. 4, 11371160 Copyright Heldermann Verlag 2016 Series of Convex Functions: Subdifferential, Conjugate and Applications to Entropy Minimization Claude Vallée Laboratoire de Mécanique des Solides, Bd M. et P. Curie, Téléport 2  BP 30179, 86962 FuturoscopeChasseneuil, France vallee@lms.univpoitiers.fr Constantin Zalinescu University Alexandru Ioan Cuza, Faculty of Mathematics, 700506 Iasi, Romania and: Institute of Mathematics O. Mayer, Romanian Academy of Sciences, Iasi, Romania zalinesc@uaic.ro A formula for the subdifferential of the sum of a series of convex functions defined on a Banach space was provided by X. Y. Zheng in 1998. In this paper, besides a slight extension to locally convex spaces of Zheng's results, we provide a formula for the conjugate of a countable sum of convex functions. Then we use these results for calculating the subdifferentials and the conjugates in two situations related to entropy minimization, and we study a concrete example met in Statistical Physics. Keywords: Series of convex functions, subdifferential, conjugate, entropy minimization, statistical physics. [ Fulltextpdf (228 KB)] for subscribers only. 