A three-term conjugate gradient method with sufficient descent property for unconstrained optimization

Yasushi Narushima, Hiroshi Yabe, John A. Ford

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

Conjugate gradient methods are widely used f or solving large-scale unconstrained optimization problems because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed method. Moreover, we present a specific three-term conjugate gradient method based on the multistep quasi-Newton method. Finally, some numerical results of the proposed method are given.

Original languageEnglish
Pages (from-to)212-230
Number of pages19
JournalSIAM Journal on Optimization
Volume21
Issue number1
DOIs
Publication statusPublished - 2011 May 30
Externally publishedYes

Fingerprint

Conjugate gradient method
Unconstrained Optimization
Conjugate Gradient Method
Descent
Sufficient
Term
Multistep Methods
Large-scale Optimization
Quasi-Newton Method
Newton-Raphson method
Global Convergence
Optimization Problem
Numerical Results
Sufficient Conditions

Keywords

  • Global convergence
  • Sufficient descent condition
  • Three-term conjugate gradient method
  • Unconstrained optimization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

Cite this

A three-term conjugate gradient method with sufficient descent property for unconstrained optimization. / Narushima, Yasushi; Yabe, Hiroshi; Ford, John A.

In: SIAM Journal on Optimization, Vol. 21, No. 1, 30.05.2011, p. 212-230.

Research output: Contribution to journalArticle

@article{d168f462c32e46658e8c513b829f9c91,
title = "A three-term conjugate gradient method with sufficient descent property for unconstrained optimization",
abstract = "Conjugate gradient methods are widely used f or solving large-scale unconstrained optimization problems because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed method. Moreover, we present a specific three-term conjugate gradient method based on the multistep quasi-Newton method. Finally, some numerical results of the proposed method are given.",
keywords = "Global convergence, Sufficient descent condition, Three-term conjugate gradient method, Unconstrained optimization",
author = "Yasushi Narushima and Hiroshi Yabe and Ford, {John A.}",
year = "2011",
month = "5",
day = "30",
doi = "10.1137/080743573",
language = "English",
volume = "21",
pages = "212--230",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - A three-term conjugate gradient method with sufficient descent property for unconstrained optimization

AU - Narushima, Yasushi

AU - Yabe, Hiroshi

AU - Ford, John A.

PY - 2011/5/30

Y1 - 2011/5/30

N2 - Conjugate gradient methods are widely used f or solving large-scale unconstrained optimization problems because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed method. Moreover, we present a specific three-term conjugate gradient method based on the multistep quasi-Newton method. Finally, some numerical results of the proposed method are given.

AB - Conjugate gradient methods are widely used f or solving large-scale unconstrained optimization problems because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed method. Moreover, we present a specific three-term conjugate gradient method based on the multistep quasi-Newton method. Finally, some numerical results of the proposed method are given.

KW - Global convergence

KW - Sufficient descent condition

KW - Three-term conjugate gradient method

KW - Unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=79957454185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957454185&partnerID=8YFLogxK

U2 - 10.1137/080743573

DO - 10.1137/080743573

M3 - Article

AN - SCOPUS:79957454185

VL - 21

SP - 212

EP - 230

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

SN - 1052-6234

IS - 1

ER -