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A modified nonmonotone trust region line search method

Abstract

Hybridizing monotone and nonmonotone approaches, we propose a modified trust region ratio in which more reasonable information is provided about consistency between the exact and the approximate models. Also, we employ an Armijo-type line search strategy to avoid resolving the trust region subproblem whenever a trial step is rejected. We show that the proposed algorithm can preserve global convergence of the traditional trust region algorithm as well as the superlinear convergence property. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr library. They demonstrate practical efficiency of the proposed algorithm in the sense of the Dolan–Moré performance profile.

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Acknowledgements

The authors thank the Research Council of Semnan University for its support. They are also grateful to the anonymous reviewers for their valuable comments and suggestions helped to improve the quality of this work.

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Correspondence to Saman Babaie-Kafaki.

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Rezaee, S., Babaie-Kafaki, S. A modified nonmonotone trust region line search method. J. Appl. Math. Comput. 57, 421–436 (2018). https://doi.org/10.1007/s12190-017-1113-4

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Keywords

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

Mathematics Subject Classifications

  • 49M37
  • 65K05
  • 90C53