nonsmooth system

A Family of Newton Methods for Nonsmooth Constrained Systems with Nonisolated Solutions

  • Francisco Facchinei
  • Andreas Fischer
  • Markus Herrich
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    We propose a new family of Newton-type methods for the solution of constrained systems of equations. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, local, quadratic convergence to a solution of the system of equations can be established. We show that as particular instances of the method we obtain inexact … Read more

    An LP-Newton Method: Nonsmooth Equations, KKT Systems, and Nonisolated Solutions

  • Francisco Facchinei
  • Andreas Fischer
  • Markus Herrich
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. … Read more