Elizabeth Wegner Karas

On the convergence rate of the Cauchy algorithm in the l2 norm

  • Elizabeth Wegner Karas
  • Ademir A. Ribeiro
  • Alessandra M. Mota
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This paper presents a convergence rate for the sequence generated by the Cauchy algorithm. The method is applied to a convex quadratic function with exact line search. Instead of using the norm induced by the hessian matrix, the q-linear convergence is shown for the l2 (or Euclidean) norm. CitationTecnhical Report, Dep. Mathematics, Federal University of … Read more

    A globally convergent filter method for nonlinear programming

  • Clóvis Caesar Gonzaga
  • Elizabeth Wegner Karas
  • Marcia Vanti
    • Categories Constrained Nonlinear Optimization Tags , ,

    In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally … Read more

    Examples of ill-behaved central paths in convex optimization

  • Jean Charles Gilbert
  • Clóvis Caesar Gonzaga
  • Elizabeth Wegner Karas
    • Categories Convex Optimization, Nonlinear Optimization

    This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data. CitationRapport de recherche 4179, INRIA, France, 2001ArticleDownload View PDF