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

C. Vallee; C. Zalinescu

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

Optimization and Control 2015-06-04 v1

Authors: C. Vallee , C. Zalinescu

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.

Keywords

convex functions series subdifferential conjugate entropy minimization Banach space locally convex spaces

Cite

@article{arxiv.1506.01216,
  title  = {Series of convex functions: subdifferential, conjugate and applications to entropy minimization},
  author = {C. Vallee and C. Zalinescu},
  journal= {arXiv preprint arXiv:1506.01216},
  year   = {2015}
}

Comments

To appear in Journal of Convex Analysis

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