{
  "id": "1606.02155",
  "version": "v1",
  "published": "2016-06-06T16:09:35.000Z",
  "updated": "2016-06-06T16:09:35.000Z",
  "title": "Orlicz addition for measures and an optimization problem for the $f$-divergence",
  "authors": [
    "Shaoxiong Hou",
    "Deping Ye"
  ],
  "categories": [
    "math.MG",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-06T16:09:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimization problem",
      "divergence",
      "dual functional orlicz affine",
      "establish functional affine isoperimetric inequalities",
      "dual functional orlicz-brunn-minkowski inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}