eprintid: 13649
rev_number: 7
eprint_status: archive
userid: 353
dir: disk0/00/01/36/49
datestamp: 2016-08-09 13:59:08
lastmod: 2021-08-27 17:41:29
status_changed: 2016-08-09 13:59:08
type: article
metadata_visibility: show
item_issues_count: 1
creators_name: Nazareth, J.L.
creators_id: AL1035
title: The method of successive affine reduction for nonlinear minimization
ispublished: pub
keywords: conjugate gradients; high-dimensional optimization; Nonlinear minimization; successive affine reduction; variable storage algorithms
abstract: The traditional development of conjugate gradient (CG) methods emphasizes notions of conjugacy and the minimization of quadratic functions. The associated theory of conjugate direction methods, strictly a branch of numerical linear algebra, is both elegant and useful for obtaining insight into algorithms for nonlinear minimization. Nevertheless, it is preferable that favorable behavior on a quadratic be a consquence of a more general approach, one which fits in more naturally with Newton and variable metric methods. We give new CG algorithms along these lines and discuss some of their properties, along with some numerical supporting evidence.
date: 1986-07-19
date_type: published
id_number: 10.1007/BF01589444
creators_browse_id: 2226
full_text_status: none
publication: Mathematical Programming
volume: 35
number: 1
pagerange: 97-109
refereed: TRUE
issn: 0025-5610
coversheets_dirty: FALSE
fp7_project: no
fp7_type: info:eu-repo/semantics/article
citation:   Nazareth, J.L. <https://pure.iiasa.ac.at/view/iiasa/2226.html>  (1986).  The method of successive affine reduction for nonlinear minimization.   Mathematical Programming 35 (1) 97-109. 10.1007/BF01589444 <https://doi.org/10.1007/BF01589444>.