{
  "id": "1601.02239",
  "version": "v1",
  "published": "2016-01-10T17:45:45.000Z",
  "updated": "2016-01-10T17:45:45.000Z",
  "title": "On minimax theorems for lower semicontinuous functions in Hilbert spaces",
  "authors": [
    "Ewa M. Bednarczuk",
    "Monika Syga"
  ],
  "comment": "13 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\\Phi$-convex functions. These conditions are expressed in terms of abstract $\\Phi$-subgradients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-10T17:45:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32F17",
      "49J52",
      "49K27",
      "49K35",
      "52A01"
    ],
    "keywords": [
      "lower semicontinuous functions",
      "hilbert space",
      "minimax theorems",
      "convex functions",
      "main tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102239B"
    }
  }
}