Summary
This chapter could be called a primer on convexity for probabilists, since it brings together some of the theory of convex functions with a view toward applications to information theory. In particular, a certain number of classical convexity inequalities (such as Jensen’s and Young’s inequalities) are presented in a unified framework thanks to the use of Bregman’s divergences.
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Collet, JF. (2018). Prelude: a user’s guide to convexity. In: Discrete Stochastic Processes and Applications. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-74018-8_6
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DOI: https://doi.org/10.1007/978-3-319-74018-8_6
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-74018-8
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