{
  "id": "1905.01893",
  "version": "v1",
  "published": "2019-05-06T09:19:22.000Z",
  "updated": "2019-05-06T09:19:22.000Z",
  "title": "A comparison of first-order methods for the numerical solution of or-constrained optimization problems",
  "authors": [
    "Patrick Mehlitz"
  ],
  "comment": "41 pages, 7 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "Mathematical programs with or-constraints form a new class of disjunctive optimization problems with inherent practical relevance. In this paper, we provide a comparison of three different first-order methods for the numerical treatment of this problem class which are inspired by classical approaches from disjunctive programming. First, we study the replacement of the or-constraints as nonlinear inequality constraints using suitable NCP-functions. Second, we transfer the or-constrained program into a mathematical program with switching or complementarity constraints which can be treated with the aid of well-known relaxation methods. Third, a direct Scholtes-type relaxation of the or-constraints is investigated. A numerical comparison of all these approaches which is based on three essentially different model programs from or-constrained optimization closes the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-06T09:19:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K05",
      "90C30",
      "90C33"
    ],
    "keywords": [
      "or-constrained optimization problems",
      "first-order methods",
      "numerical solution",
      "comparison",
      "direct scholtes-type relaxation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}