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Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch

Abstract

In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.

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Correspondence to Da-chuan Xu.

Additional information

Partly supported by the National Natural Sciences Foundation of China (No. 19731001), Natural 973 Information Technology and High-Performance Software Program of China (No. G1998030401) and K. C. Wong Education Foundation, Hong Kong.

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Xu, Dc. Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch. Acta Mathematicae Applicatae Sinica, English Series 19, 19–24 (2003). https://doi.org/10.1007/s10255-003-0076-4

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  • DOI: https://doi.org/10.1007/s10255-003-0076-4

Keywords

  • Quasi-Newton method
  • Broyden class
  • non-monotone linesearch
  • global convergence
  • unconstrained optimization

2000 MR Subject Classification

  • 65K
  • 90C