{
  "id": "2201.04175",
  "version": "v1",
  "published": "2022-01-11T19:52:56.000Z",
  "updated": "2022-01-11T19:52:56.000Z",
  "title": "A generalization of the Moreau-Yosida regularization",
  "authors": [
    "Aras Bacho"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "For a function $f:X \\rightarrow (-\\infty,+\\infty]$ on a normed space $(X,\\Vert \\cdot \\Vert)$ and given parameters $p>1$ and $\\varepsilon>0$, we investigate the properties of the generalized Moreau-Yosida regularization given by \\begin{align*} f_\\varepsilon(u)=\\inf_{v\\in X}\\left\\lbrace \\frac{1}{p\\varepsilon} \\Vert u-v\\Vert^p+f(v)\\right\\rbrace \\quad ,u\\in X. \\end{align*} We show that the generalized Moreau-Yosida regularization satisfies the same properties as in the classical case for $p=2$ provided $X$ is not a Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-11T19:52:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalization",
      "generalized moreau-yosida regularization satisfies",
      "properties",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}