{
  "id": "2001.06511",
  "version": "v1",
  "published": "2020-01-17T20:03:11.000Z",
  "updated": "2020-01-17T20:03:11.000Z",
  "title": "A perturbation view of level-set methods for convex optimization",
  "authors": [
    "Ron Estrin",
    "Michael P. Friedlander"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $\\epsilon$-infeasible points that do not converge to a feasible point as $\\epsilon$ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater's constraint qualification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-17T20:03:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "65K10",
      "49M29"
    ],
    "keywords": [
      "convex optimization",
      "perturbation view",
      "strong duality",
      "level-set approach",
      "level-set method identifies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}