Error bounds

Primal-dual global convergence of an augmented Lagrangian method under the error bound condition

  • Roberto Andreani
  • Gabriel Haeser
  • Renan W. Prado
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    This work investigates global convergence properties of a safeguarded augmented Lagrangian method applied to nonlinear programming problems, with an emphasis on the role of constraint qualifications in ensuring boundedness of the Lagrange multiplier estimates, also known as dual sequences. When functions with locally Lipschitz continuous derivatives define the constraint set, we prove that the Error … Read more

    On complexity constants of linear and quadratic models for derivative-free trust-region algorithms

  • A. E. Schwertner
  • Francisco N. C. Sobral
    • Categories Nonlinear Optimization Tags , , ,

    Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing complexity results hide the dimensions of the problem. This work organizes several results in literature about bounds that appear in derivative-free trust-region algorithms based on linear … Read more

    Convergence analysis under consistent error bounds

  • Tianxiang Liu
  • Bruno F. Lourenço
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and Holderian error bounds and includes logarithmic and entropic error bound found in the exponential cone. It also includes the error bounds obtainable under the theory of … Read more