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)


Memoryless quasi-Newton methods are studied for solving large- scale 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 con- verges globally. Finally, some numerical experiments are given.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalJournal of Industrial and Management Optimization
Issue number5
Publication statusPublished - 2017 Jan 1
Externally publishedYes


  • 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

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