Katya Scheinberg

Global Convergence of General Derivative-Free Trust-Region Algorithms to First and Second Order Critical Points

  • Andrew R. Conn
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Unconstrained Optimization Tags , , ,

    In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, … Read more

    Geometry of Sample Sets in Derivative Free Optimization. Part II: Polynomial Regression and Underdetermined Interpolation

  • Andrew R. Conn
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    In the recent years, there has been a considerable amount of work in the development of numerical methods for derivative free optimization problems. Some of this work relies on the management of the geometry of sets of sampling points for function evaluation and model building. In this paper, we continue the work developed in [Conn, … Read more

    Error Estimates and Poisedness in Multivariate Polynomial Interpolation

  • Andrew R. Conn
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    We show how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new definition of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. This definition is equivalent to … Read more