filter method – Optimization Online

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

Published: 2024/02/06

Applications - Science and Engineering, Nonlinear Optimization alternating direction method of multipliers, augmented Lagrangian, filter method, nonconvex optimization

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

Published: 2011/03/08

Yannan Chen

Wenyu Sun

Unconstrained Optimization filter method, global convergence, line-search, negative curvature direction, second-order critical point

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

Published: 2003/02/19, Updated: 2003/09/18

Nie Pu-yan

Nonlinear Optimization constrained, convergent, filter method, nonlinear programming, s method

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

Published: 2001/08/23, Updated: 2002/05/29

Lorenz T. Biegler

Andreas Wächter

Constrained Nonlinear Optimization barrier method, filter method, global convergence, interior point methods, line-search, local convergence, maratos effect, nonconvex constrained optimization, nonlinear programming, second order correction, sequential quadratic programming

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

Published: 2000/08/21, Updated: 2001/05/25

Roger Fletcher

Sven Leyffer

Convex and Nonsmooth Optimization, Nonsmooth Optimization bundle method, filter method, nonsmooth optimization

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. CitationNA\195, Department of Mathematics, University of Dundee, UK, December, 1999ArticleDownload View PDF