Geodesic
Series of Convex Functions: Subdifferential, Conjugate and Applications to Entropy Minimization
Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1137-116
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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.
Mots-clés : Series of convex functions, subdifferential, conjugate, entropy minimization, statistical physics 
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     author = {C. Vall\'ee and C. Zalinescu},
     title = {Series of {Convex} {Functions:} {Subdifferential,} {Conjugate} and {Applications} to {Entropy} {Minimization}},
     journal = {Journal of convex analysis},
     pages = {1137--116},
     year = {2016},
     volume = {23},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a6/}
}
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C. Vallée; C. Zalinescu. Series of Convex Functions: Subdifferential, Conjugate and Applications to Entropy Minimization. Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1137-116. http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a6/