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Two accelerated nonmonotone adaptive trust region line search methods

Abstract

Hybridizing monotone and nonmonotone approaches, we employ a modified trust region ratio in which more information is provided about the agreement between the exact and the approximate models. Also, we use an adaptive trust region radius as well as two accelerated Armijo-type line search strategies to avoid resolving the trust region subproblem whenever a trial step is rejected. We show that the proposed algorithm is globally and locally superlinearly convergent. Comparative numerical experiments show practical efficiency of the proposed accelerated adaptive trust region algorithm.

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Acknowledgements

This research was in part supported by the grant 95849086 from Iran National Science Foundation (INSF), and in part by the Research Council of Semnan University. The authors thank the anonymous reviewer for his/her valuable comments and suggestions helped to improve the presentation.

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Correspondence to Saman Babaie–Kafaki.

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Babaie–Kafaki, S., Rezaee, S. Two accelerated nonmonotone adaptive trust region line search methods. Numer Algor 78, 911–928 (2018). https://doi.org/10.1007/s11075-017-0406-x

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Keywords

  • Unconstrained optimization
  • Trust region method
  • Line search
  • Acceleration
  • Global convergence
  • Superlinear convergence

Mathematics Subject Classification (2010)

  • 49M37
  • 65K05
  • 90C53