Nonlinear Optimization

On reduced QP formulations of monotone LCP problems

  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Quadratic Programming Tags , ,

    Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation—one that has fewer constraints than the “standard” QP formulation—is available. We mention several instances of this class, including the known case in which the … 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