A combined class of self-scaling and modified quasi-Newton methods

Mehiddin Al-Baali, Humaid Khalfan

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Techniques for obtaining safely positive definite Hessian approximations with self-scaling and modified quasi-Newton updates are combined to obtain 'better' curvature approximations in line search methods for unconstrained optimization. It is shown that this class of methods, like the BFGS method, has the global and superlinear convergence for convex functions. Numerical experiments with this class, using the well-known quasi-Newton BFGS, DFP and a modified SR1 updates, are presented to illustrate some advantages of the new techniques. These experiments show that the performance of several combined methods are substantially better than that of the standard BFGS method. Similar improvements are also obtained if the simple sufficient function reduction condition on the steplength is used instead of the strong Wolfe conditions.

Original languageEnglish
Pages (from-to)393-408
Number of pages16
JournalComputational Optimization and Applications
Volume52
Issue number2
DOIs
Publication statusPublished - Jun 2012

Fingerprint

BFGS Method
Quasi-Newton
Quasi-Newton Method
Newton-Raphson method
Update
Scaling
Superlinear Convergence
Combined Method
Line Search
Unconstrained Optimization
Approximation
Search Methods
Global Convergence
Positive definite
Convex function
Experiments
Curvature
Numerical Experiment
Sufficient
Experiment

Keywords

  • Line-search framework
  • Modified quasi-Newton updates
  • Self-scaling technique
  • Unconstrained optimization

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization

Cite this

A combined class of self-scaling and modified quasi-Newton methods. / Al-Baali, Mehiddin; Khalfan, Humaid.

In: Computational Optimization and Applications, Vol. 52, No. 2, 06.2012, p. 393-408.

Research output: Contribution to journalArticle

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