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
A mechanism for proving global convergence infilter-type methods for nonlinear programming is described. Such methods are characterized by their use of the dominance concept of multi objective optimization, instead of a penalty parameter whose adjustment can be problematic. The main point of interest is to demonstrate how convergence for NLP can be induced without forcing … Read more
Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms do produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed … Read more