{
  "id": "1107.5280",
  "version": "v1",
  "published": "2011-07-26T18:12:59.000Z",
  "updated": "2011-07-26T18:12:59.000Z",
  "title": "A One-Dimensional Local Tuning Algorithm for Solving GO Problems with Partially Defined Constraints",
  "authors": [
    "Yaroslav D. Sergeyev",
    "Dmitri E. Kvasov",
    "Falah M. H. Khalaf"
  ],
  "comment": "15 pages, 5 figures, 4 tables",
  "journal": "Sergeyev Ya.D., Kvasov D.E., Khalaf F.M.H. (2007) A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints, Optimization Letters, 1(1), 85-99",
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA",
    "physics.comp-ph"
  ],
  "abstract": "Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified in an a priori given order fixed by the nature of the problem are studied. Moreover, if a constraint is not satisfied at a point, then the remaining constraints and the objective function can be undefined at this point. The constrained problem is reduced to a discontinuous unconstrained problem by the index scheme without introducing additional parameters or variables. A new geometric method using adaptive estimates of local Lipschitz constants is introduced. The estimates are calculated by using the local tuning technique proposed recently. Numerical experiments show quite a satisfactory performance of the new method in comparison with the penalty approach and a method using a priori given Lipschitz constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-26T18:12:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "65K05",
      "49M37",
      "90C56"
    ],
    "keywords": [
      "one-dimensional local tuning algorithm",
      "partially defined constraints",
      "lipschitz one-dimensional constrained global optimization",
      "lipschitz constants",
      "objective function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5280S"
    }
  }
}