{
  "id": "1804.05098",
  "version": "v1",
  "published": "2018-04-13T19:51:53.000Z",
  "updated": "2018-04-13T19:51:53.000Z",
  "title": "On the Differentiability of the Solution to Convex Optimization Problems",
  "authors": [
    "Shane Barratt"
  ],
  "comment": "4 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we provide conditions under which one can take derivatives of the solution to a convex optimization problem with respect to problem data. These conditions are that Slater's condition holds, the functions involved are twice differentiable, and that a certain Jacobian is nonsingular. The derivation involves applying the implicit function theorem to the necessary and sufficient KKT system for optimality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T19:51:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex optimization problem",
      "differentiability",
      "implicit function theorem",
      "slaters condition holds",
      "sufficient kkt system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}