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Title: A brief history of filter methods.

Abstract

We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective optimization problem that minimizes the objective and the constraint violation. We outline the main ideas and convergence results of filter methods and indicate other areas where filter methods have been used successfully.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
950202
Report Number(s):
ANL/MCS/JA-58300
TRN: US200910%%29
DOE Contract Number:
DE-AC02-06CH11357
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAG/OPT; Journal Volume: 18; Journal Issue: 1 ; 2007
Country of Publication:
United States
Language:
ENGLISH
Subject:
97 MATHEMATICS AND COMPUTING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONVERGENCE; ITERATIVE METHODS; NONLINEAR PROGRAMMING; OPTIMIZATION; HISTORICAL ASPECTS

Citation Formats

Fletcher, R., Leyffer, S., Toint, P., Mathematics and Computer Science, Univ. of Dundee, and Univ. of Namur. A brief history of filter methods.. United States: N. p., 2007. Web.
Fletcher, R., Leyffer, S., Toint, P., Mathematics and Computer Science, Univ. of Dundee, & Univ. of Namur. A brief history of filter methods.. United States.
Fletcher, R., Leyffer, S., Toint, P., Mathematics and Computer Science, Univ. of Dundee, and Univ. of Namur. Mon . "A brief history of filter methods.". United States. doi:.
@article{osti_950202,
title = {A brief history of filter methods.},
author = {Fletcher, R. and Leyffer, S. and Toint, P. and Mathematics and Computer Science and Univ. of Dundee and Univ. of Namur},
abstractNote = {We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective optimization problem that minimizes the objective and the constraint violation. We outline the main ideas and convergence results of filter methods and indicate other areas where filter methods have been used successfully.},
doi = {},
journal = {SIAG/OPT},
number = 1 ; 2007,
volume = 18,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}