local convergence

On the Relationship between Bilevel Decomposition Algorithms and Direct Interior-Point Methods

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization Tags , , ,

    Engineers have been using \emph{bilevel decomposition algorithms} to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upper-level problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used … Read more

    A Local Convergence Theory of a Filter Line Search Method for Nonlinear Programming

  • Choong Ming Chin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    In this paper the theory of local convergence for a class of line search filter type methods for nonlinear programming is presented. The algorithm presented here is globally convergent (see Chin [4]) and the rate of convergence is two-step superlinear. The proposed algorithm solves a sequence of quadratic progrmming subproblems to obtain search directions and … Read more

    A Simple Primal-Dual Feasible Interior-Point Methodfor Nonlinear Programming with Monotone Descent

  • Sasan Bakhtiari
  • André L. Tits
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We propose and analyze a primal-dual interior point method of the “feasible” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary … Read more

    Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming

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

    Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior … Read more