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

2015/06/03 by Vallee, C., Constantin Zălinescu, Zalinescu, C.
Computer Science · Mathematics · #49N15 #82D05 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1506.01216

openalex publication_date 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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