Wide interval for efficient self-scaling quasi-Newton algorithms

Mehiddin Al-Baali, Humaid Khalfan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This article uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstrained optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but also increase their chances of success. Self-scaling updates from the preconvex and postconvex classes are shown to be effective in practice, and new algorithms, which work well in practice with or without scaling, are also obtained from the new interval. Unlike the behavior of unscaled methods, numerical testing shows that varying the updating parameter in the proposed interval has little effect on the performance of the self-scaling algorithms.

Original languageEnglish
Pages (from-to)679-691
Number of pages13
JournalOptimization Methods and Software
Volume20
Issue number6
DOIs
Publication statusPublished - Dec 2005

Fingerprint

Quasi-Newton Algorithm
Scaling
Interval
Update
Testing
Superlinear Convergence
Unconstrained Optimization
Numerical methods
Global Convergence
Accelerate
Updating
Two Parameters
Numerical Methods

Keywords

  • Broyden's family
  • Global and superlinear convergence
  • Quasi-Newton methods
  • Self-scaling
  • Unconstrained optimization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

Cite this

Wide interval for efficient self-scaling quasi-Newton algorithms. / Al-Baali, Mehiddin; Khalfan, Humaid.

In: Optimization Methods and Software, Vol. 20, No. 6, 12.2005, p. 679-691.

Research output: Contribution to journalArticle

@article{cd5bd988bca24c55805acb5f08d2f54e,
title = "Wide interval for efficient self-scaling quasi-Newton algorithms",
abstract = "This article uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstrained optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but also increase their chances of success. Self-scaling updates from the preconvex and postconvex classes are shown to be effective in practice, and new algorithms, which work well in practice with or without scaling, are also obtained from the new interval. Unlike the behavior of unscaled methods, numerical testing shows that varying the updating parameter in the proposed interval has little effect on the performance of the self-scaling algorithms.",
keywords = "Broyden's family, Global and superlinear convergence, Quasi-Newton methods, Self-scaling, Unconstrained optimization",
author = "Mehiddin Al-Baali and Humaid Khalfan",
year = "2005",
month = "12",
doi = "10.1080/10556780410001709448",
language = "English",
volume = "20",
pages = "679--691",
journal = "Optimization Methods and Software",
issn = "1055-6788",
publisher = "Taylor and Francis Ltd.",
number = "6",

}

TY - JOUR

T1 - Wide interval for efficient self-scaling quasi-Newton algorithms

AU - Al-Baali, Mehiddin

AU - Khalfan, Humaid

PY - 2005/12

Y1 - 2005/12

N2 - This article uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstrained optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but also increase their chances of success. Self-scaling updates from the preconvex and postconvex classes are shown to be effective in practice, and new algorithms, which work well in practice with or without scaling, are also obtained from the new interval. Unlike the behavior of unscaled methods, numerical testing shows that varying the updating parameter in the proposed interval has little effect on the performance of the self-scaling algorithms.

AB - This article uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstrained optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but also increase their chances of success. Self-scaling updates from the preconvex and postconvex classes are shown to be effective in practice, and new algorithms, which work well in practice with or without scaling, are also obtained from the new interval. Unlike the behavior of unscaled methods, numerical testing shows that varying the updating parameter in the proposed interval has little effect on the performance of the self-scaling algorithms.

KW - Broyden's family

KW - Global and superlinear convergence

KW - Quasi-Newton methods

KW - Self-scaling

KW - Unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=29744452629&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29744452629&partnerID=8YFLogxK

U2 - 10.1080/10556780410001709448

DO - 10.1080/10556780410001709448

M3 - Article

AN - SCOPUS:29744452629

VL - 20

SP - 679

EP - 691

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 6

ER -