Memoryless quasi-newton methods based on spectral-scaling broyden family for unconstrained optimization

Shummin Nakayama, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Memoryless quasi-Newton methods are studied for solving largescale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, and we show that the proposed method satisfies the sufficient descent condition and converges globally. Finally, some numerical experiments are given.

Original languageEnglish
Pages (from-to)1773-1793
Number of pages21
JournalJournal of Industrial and Management Optimization
Volume15
Issue number4
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes

Fingerprint

Quasi-Newton Method
Unconstrained Optimization
Newton-Raphson method
Scaling
Conjugate gradient method
Conjugate Gradient Method
Chord or secant line
Descent
Updating
Numerical Experiment
Sufficient
Optimization Problem
Converge
Family
Experiments

Keywords

  • Broyden family
  • Global convergence
  • Memoryless quasi-Newton method
  • Sufficient descent condition
  • Unconstrained optimization

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics

Cite this

Memoryless quasi-newton methods based on spectral-scaling broyden family for unconstrained optimization. / Nakayama, Shummin; Narushima, Yasushi; Yabe, Hiroshi.

In: Journal of Industrial and Management Optimization, Vol. 15, No. 4, 01.01.2019, p. 1773-1793.

Research output: Contribution to journalArticle

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