Marcelo Marazzi

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

    Feasibility Control in Nonlinear Optimization

  • Marcelo Marazzi
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization Tags ,

    We analyze the properties that optimization algorithms must possess in order to prevent convergence to non-stationary points for the merit function. We show that demanding the exact satisfaction of constraint linearizations results in difficulties in a wide range of optimization algorithms. Feasibility control is a mechanism that prevents convergence to spurious solutions by ensuring that … Read more