nonlinear optimization

Augmented self concordant barriers and nonlinear optimization problems with finite complexity

  • Yurii Nesterov
  • Jean-Philippe Vial
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratic form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the complexity of finding the analytic center … Read more

    Failure of Global Convergence for a Class of Interior Point Methods for Nonlinear Programming

  • Lorenz T. Biegler
  • Andreas Wächter
    • Categories Nonlinear Optimization Tags , ,

    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