{
  "id": "1503.02753",
  "version": "v1",
  "published": "2015-03-10T02:17:57.000Z",
  "updated": "2015-03-10T02:17:57.000Z",
  "title": "A semi-smooth Newton method for solving convex quadratic programming problem under simplicial cone constraint",
  "authors": [
    "J. G. Barrios",
    "O. P. Ferreira",
    "S. Z. Németh"
  ],
  "comment": "17 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an equivalence between the simplicial cone constrained convex quadratic programming problem and the one of finding the unique solution of a nonsmooth system of equations. It is shown that a semi-smooth Newton method applied to this nonsmooth system of equations is always well defined and under a mild assumption on the simplicial cone the method generates a sequence that converges linearly to its solution. Besides, we also show that the generated sequence is bounded for any starting point and a formula for any accumulation point of this sequence is presented. The presented numerical results suggest that this approach achieves accurate solutions to large problems in few iterations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-10T02:17:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C33",
      "15A48"
    ],
    "keywords": [
      "solving convex quadratic programming problem",
      "semi-smooth newton method",
      "cone constrained convex quadratic",
      "constrained convex quadratic programming",
      "simplicial cone constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}