Series of convex functions: subdifferential, conjugate and applications to entropy minimization

C. Vallee; C. Zalinescu

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arXiv · 1506.01216

Series of convex functions: subdifferential, conjugate and applications to entropy minimization

C. Vallee·C. Zalinescu

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Abstract

A formula for the sub\-differential 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 sub\-differentials and the conjugates in two situations related to entropy minimization, and we study a concrete example met in Statistical Physics.

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BibTeX RIS

C. Vallee, C. Zalinescu. 2015-06-03. Series of convex functions: subdifferential, conjugate and applications to entropy minimization. https://arxiv.org/abs/1506.01216

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