{
  "id": "0911.1182",
  "version": "v1",
  "published": "2009-11-06T05:50:11.000Z",
  "updated": "2009-11-06T05:50:11.000Z",
  "title": "On representations of the feasible set in convex optimization",
  "authors": [
    "Jean B. Lasserre"
  ],
  "comment": "to appear in Optimization Letters",
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider the convex optimization problem $\\min \\{f(x) : g_j(x)\\leq 0, j=1,...,m\\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-06T05:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "65K05"
    ],
    "keywords": [
      "feasible set",
      "representation",
      "kkt point",
      "slaters condition holds",
      "kkt optimality conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1182L"
    }
  }
}