filter method

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

  • Robert Baraldi
  • Stefan M. Wild
  • Sven Leyffer
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    Nonconvex, nonlinear cost functions arise naturally in physical inverse problems and machine learning. The alternating direction method of multipliers (ADMM) has seen extensive use in these applications, despite exhibiting uncertain convergence behavior in many practical nonconvex settings, and struggling with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential … Read more

    A Dwindling Filter Line Search Method for Unconstrained Optimization

  • Yannan Chen
  • Wenyu Sun
    • Categories Unconstrained Optimization Tags , , , ,

    In this paper, we propose a new dwindling multidimensional filter second-order line search method for solving large-scale unconstrained optimization problems. Usually, the multidimensional filter is constructed with a fixed envelope, which is a strict condition for the gradient vectors. A dwindling multidimensional filter technique, which is a modification and improvement of the original multidimensional filter, … Read more

    Sequential Penalty Quadratic Programming Filter Methods for Nonlinear Programming

  • Nie Pu-yan
    • Categories Nonlinear Optimization Tags , , , ,

    Filter approach is recently proposed by Fletcher and Leyffer in 2002 and is attached importance to. In this paper, the filter approach is used in an sequential penalty quadratic programming (S$l$QP) algorithm which is similar to that of Yuan’s. In every trial step, the step length is controlled by a trust region radius. If the … 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

    A bundle filter method for nonsmooth nonlinear optimization

  • Roger Fletcher
  • Sven Leyffer
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We consider minimizing a nonsmooth objective subject to nonsmooth constraints. The nonsmooth functions are approximated by a bundle of subgradients. The novel idea of a filter is used to promote global convergence. Citation NA\195, Department of Mathematics, University of Dundee, UK, December, 1999 Article Download View A bundle filter method for nonsmooth nonlinear optimization