A MEMORYLESS SYMMETRIC RANK-ONE METHOD WITH SUFFICIENT DESCENT PROPERTY FOR UNCONSTRAINED OPTIMIZATION

• Nakayama Shummin

  Tokyo University of Science

• Narushima Yasushi

  Yokohama National University

• Yabe Hiroshi

  Tokyo University of Science

Abstract

Quasi-Newton methods are widely used for solving unconstrained optimization problems. However, it is difficult to apply quasi-Newton methods directly to large-scale unconstrained optimization problems, because they need the storage of memories for matrices. In order to overcome this difficulty, memoryless quasi-Newton methods were proposed. Shanno (1978) derived the memoryless BFGS method. Recently, several researchers studied the memoryless quasi-Newton method based on the symmetric rank-one formula. However existing memoryless symmetric rank-one methods do not necessarily satisfy the sufficient descent condition. In this paper, we focus on the symmetric rank-one formula based on the spectral scaling secant condition and derive a memoryless quasi-Newton method based on the formula. Moreover we show that the method always satisfies the sufficient descent condition and converges globally for general objective functions. Finally, preliminary numerical results are shown.

Journal

• Journal of the Operations Research Society of Japan

  Journal of the Operations Research Society of Japan 61 (1), 53-70, 2018

  The Operations Research Society of Japan

Keywords

• Nonlinear programming
• unconstrained optimization
• memoryless quasi-Newton method
• symmetric rank-one formula
• sufficient descent condition

Details

• CRID: 1390001204111498112
• NII Article ID: 130006301100
• NII Book ID: AA00703935
• DOI: 10.15807/jorsj.61.53
• ISSN: 21888299
• ISSN: 04534514
• NDL BIB ID: 028775525
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I028775525
• Web Site: https://www.jstage.jst.go.jp/article/jorsj/61/1/61_53/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed