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

@inproceedings{Hou2016OrliczAF,
  title={Orlicz addition for measures and an optimization problem for the \$f\$-divergence},
  author={Shaoxiong Hou and Deping Ye},
  year={2016}
}
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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