{
  "id": "1802.03046",
  "version": "v1",
  "published": "2018-02-08T20:58:32.000Z",
  "updated": "2018-02-08T20:58:32.000Z",
  "title": "Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle",
  "authors": [
    "M. V. Dolgopolik"
  ],
  "comment": "This is a slightly editer verion of a pre-print of an article published in Mathematical Programming. The final authenticated version is available online at: https://doi.org/10.1007/s10107-017-1122-y In this version, a mistake in the proof of Theorem 4 was corrected",
  "journal": "Mathematical Programming, 166:1-2 (2017) 297-326",
  "doi": "10.1007/s10107-017-1122-y",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this article, we present new general results on existence of augmented Lagrange multipliers. We define a penalty function associated with an augmented Lagrangian, and prove that, under a certain growth assumption on the augmenting function, an augmented Lagrange multiplier exists if and only if this penalty function is exact. We also develop a new general approach to the study of augmented Lagrange multipliers called the localization principle. The localization principle allows one to study the local behaviour of the augmented Lagrangian near globally optimal solutions of the initial optimization problem in order to prove the existence of augmented Lagrange multipliers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-08T20:58:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C30",
      "65K05"
    ],
    "keywords": [
      "augmented lagrange multiplier",
      "exact penalty functions",
      "localization principle",
      "initial optimization problem",
      "augmented lagrangian"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}