Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

Hiroshi Kobayashi, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticle

Abstract

The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.

Original languageEnglish
Pages (from-to)1313-1329
Number of pages17
JournalOptimization Methods and Software
Volume32
Issue number6
DOIs
Publication statusPublished - 2017 Nov 2
Externally publishedYes

Fingerprint

Conjugate gradient method
Unconstrained Optimization
Conjugate Gradient Method
Chord or secant line
Descent
Term
Sufficient
Large-scale Optimization
Global Convergence
Convergence Properties
Optimization Problem
Numerical Results

Keywords

  • global convergence
  • secant condition
  • sufficient descent property
  • three-term conjugate gradient method
  • unconstrained optimization

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics

Cite this

Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization. / Kobayashi, Hiroshi; Narushima, Yasushi; Yabe, Hiroshi.

In: Optimization Methods and Software, Vol. 32, No. 6, 02.11.2017, p. 1313-1329.

Research output: Contribution to journalArticle

@article{4a060f3331c743d1906414d464c6c814,
title = "Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization",
abstract = "The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.",
keywords = "global convergence, secant condition, sufficient descent property, three-term conjugate gradient method, unconstrained optimization",
author = "Hiroshi Kobayashi and Yasushi Narushima and Hiroshi Yabe",
year = "2017",
month = "11",
day = "2",
doi = "10.1080/10556788.2017.1338288",
language = "English",
volume = "32",
pages = "1313--1329",
journal = "Optimization Methods and Software",
issn = "1055-6788",
publisher = "Taylor and Francis Ltd.",
number = "6",

}

TY - JOUR

T1 - Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

AU - Kobayashi, Hiroshi

AU - Narushima, Yasushi

AU - Yabe, Hiroshi

PY - 2017/11/2

Y1 - 2017/11/2

N2 - The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.

AB - The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.

KW - global convergence

KW - secant condition

KW - sufficient descent property

KW - three-term conjugate gradient method

KW - unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=85021136549&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021136549&partnerID=8YFLogxK

U2 - 10.1080/10556788.2017.1338288

DO - 10.1080/10556788.2017.1338288

M3 - Article

AN - SCOPUS:85021136549

VL - 32

SP - 1313

EP - 1329

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 6

ER -