Nonlinear Systems and Least-Squares

On the Convergence of Newton Iterations to Non-Stationary Points

  • Richard H. Byrd
  • Marcelo Marazzi
  • Jorge Nocedal
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    We study conditions under which line search Newton methods for nonlinear systems of equations and optimization fail due to the presence of singular non-stationary points. These points are not solutions of the problem and are characterized by the fact that Jacobian or Hessian matrices are singular. It is shown that, for systems of nonlinear equations, … Read more

    Reducing the number of AD passes for computing a sparse Jacobian matrix

  • Shahadat Hossain
  • Trond Steihaug
    • Categories Graphs and Matroids, Nonlinear Systems and Least-Squares Tags , ,

    A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution … Read more