Nicolas F. Armijo

A semi-smooth Newton method for general projection equations applied to the nearest correlation matrix problem

  • Nicolas F. Armijo
  • Yunier Bello-Cruz
  • Gabriel Haeser
    • Categories Semi-definite Programming Tags , , ,

    In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke’s generalized Jacobian of the projection onto a closed and convex cone. We then describe the iterative process for the general cone case and establish … Read more

    On the convergence of iterative schemes for solving a piecewise linear system of equations

  • Nicolas F. Armijo
  • Yunier Bello-Cruz
  • Gabriel Haeser
    • Categories Nonlinear Systems and Least-Squares Tags , ,

    This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first provide a negative answer via a counterexample to a conjecture on the global and finite convergence of the Newton iteration … Read more