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arXiv · 1606.02155

Orlicz addition for measures and an optimization problem for the $f$-divergence

Shaoxiong Hou·Deping Ye
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Abstract

In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional Orlicz-Brunn-Minkowski inequality, are established. We also investigate an optimization problem for the $f$-divergence and establish functional affine isoperimetric inequalities for the dual functional Orlicz affine and geominimal surface areas of measures.

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Shaoxiong Hou, Deping Ye. 2016-06-06. Orlicz addition for measures and an optimization problem for the $f$-divergence. https://arxiv.org/abs/1606.02155

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