Abstract

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.

Author information

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

Claude Vallée

Laboratoire de Mécanique des Solides, Bd M. et P. Curie, Téléport 2 - BP 30179, 86962 Futuroscope-Chasseneuil, France

vallee@lms.univ-poitiers.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

Keywords

  • Series of convex functions
  • subdifferential
  • conjugate
  • entropy minimization
  • statistical physics

Suggested citation

C. Vallée, C. Zalinescu. “Series of Convex Functions: Subdifferential, Conjugate and Applications to Entropy Minimization.” Journal of Convex Analysis 23 (2016), No. 4, 1137–1160.

Copyright Banach Press 2016