eprintid: 14158
rev_number: 5
eprint_status: archive
userid: 5
dir: disk0/00/01/41/58
datestamp: 2016-12-14 12:47:38
lastmod: 2021-08-27 17:28:17
status_changed: 2016-12-14 12:47:38
type: article
metadata_visibility: show
item_issues_count: 3
creators_name: Gilbert, J.C.
creators_id: AL0691
title: Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization
ispublished: pub
divisions: prog_mda
keywords: Augmented Lagrangian; constrained optimization; exact penalty function; global convergence; optimization algorithm; reduced secant method; superlinear convergence; Wolfe's step-size selection
abstract: We propose an algorithm for minimizing a functionf on ℝn in the presence ofm equality constraintsc that locally is a reduced secant method. The local method is globalized using a nondifferentiable augmented Lagrangian whose decrease is obtained by both a longitudinal search that decreases mainlyf and a transversal search that decreases mainly ∥c∥. Our main objective is to show that the longitudinal path can be designed to maintain the positive definiteness of the reduced matrices by means of the positivity ofγkTδk, whereγk is the change in the reduced gradient and δk is the reduced longitudinal displacement.
date: 1991
date_type: published
publisher: Springer
id_number: 10.1007/BF01594922
creators_browse_id: 1903
full_text_status: none
publication: Mathematical Programming
volume: 50
number: 1-3
pagerange: 1-28
refereed: TRUE
issn: 0025-5610
coversheets_dirty: FALSE
fp7_type: info:eu-repo/semantics/article
citation:   Gilbert, J.C. <https://pure.iiasa.ac.at/view/iiasa/1903.html>  (1991).  Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization.   Mathematical Programming 50 (1-3) 1-28. 10.1007/BF01594922 <https://doi.org/10.1007/BF01594922>.