On Exponentially Concave Functions and Their Impact in Information Theory


G. Alirezaei, R. Mathar,


        Concave functions play a central role in optimiza tion. So-called exponentially concave functions are of similar importance in information theory. In this paper, we comprehensively discuss mathematical properties of the class of exponentially concave functions, like closedness under linear and convex combination and relations to quasi-, Jensen- and Schur-concavity. Information theoretic quantities such as self-information and (scaled) entropy are shown to be exponentially concave. Furthermore, new inequalities for the Kullback-Leibler divergence, for the entropy of mixture distributions, and for mutual information are derived.

Index Terms

Inequalities, convex optimization, Schurconcave, quasiconcave, Shannon theory, self-information, entropy, mutual information, divergence, mixture distribution

BibTEX Reference Entry 

	author = {Gholamreza Alirezaei and Rudolf Mathar},
	title = "On Exponentially Concave Functions and Their Impact in Information Theory",
	pages = "10",
	booktitle = "Information Theory and Applications Workshop (ITA'18)",
	address = {San Diego, California, USA},
	month = Feb,
	year = 2018,
	hsb = RWTH-2018-221469,


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