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Series of convex functions: subdifferential, conjugate and applications to entropy minimization
- Publication Year :
- 2015
-
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.<br />Comment: To appear in Journal of Convex Analysis
- Subjects :
- Mathematics - Optimization and Control
90C25, 49N15, 82D05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1506.01216
- Document Type :
- Working Paper