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Journal of Convex Analysis 23 (2016), No. 4, 1137--1160
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 Futuroscope-Chasseneuil, France

Constantin Zalinescu
University Alexandru Ioan Cuza, Faculty of Mathematics, 700506 Iasi, Romania
and: Institute of Mathematics O. Mayer, Romanian Academy of Sciences, Iasi, Romania

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.

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