{
  "id": "1805.03009",
  "version": "v1",
  "published": "2018-05-08T13:39:59.000Z",
  "updated": "2018-05-08T13:39:59.000Z",
  "title": "The Semi-Smooth Newton Method for a Class of Variational Inequalities",
  "authors": [
    "Veronika Karl",
    "Frank Pörner"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this article we consider the semi-smooth Newton method for a class of variational inequalities. This class includes important problems like control constrained optimal control problems and state constrained optimal control problems in its penalized formulation. Moreover, Nash equilibrium problems are contained and the obstacle problem in its regularized dual formulation. We rewrite the variational inequality into a system of nonlinear equations and establish superlinear convergence for the associated Newton method. We also provide finite element discretizations for some important examples. Several numerical examples are presented to support the theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-08T13:39:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M05",
      "49M15",
      "65K10",
      "65K15"
    ],
    "keywords": [
      "semi-smooth newton method",
      "variational inequality",
      "control constrained optimal control problems",
      "state constrained optimal control problems",
      "finite element discretizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}