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pp 1–34 | Cite as

A new nonmonotone line-search trust-region approach for nonlinear systems

  • Morteza KimiaeiEmail author
  • Farzad Rahpeymaii
Original Paper
  • 15 Downloads

Abstract

This paper introduces a new derivative-free trust-region algorithm for solving nonlinear systems, based on a new nonmonotone technique and an adaptive radius strategy. It is shown that we can generate the small (large) steps and radii in the cases where iterations are near (far away from) the optimizer. Such a nonmonotone strategy is embedded into the trust region framework and Armijo line search to face with problems which have the narrow curved valley. To prevent resolving the trust-region subproblem, the nonmonotone Armijo line search is used whenever iterations are unsuccessful. In each iteration, the adaptive radius strategy is constructed based on the norm of the best function values. The global and q-quadratic rate of convergence of the new algorithm is proved. Computational results are reported.

Keywords

Nonlinear equations Derivative-free optimization Trust-region framework Adaptive radius strategy Line-search method Nonmonotone technique Global convergence 

Mathematics Subject Classification

65K05 90C25 90C06 94A08 

Notes

Acknowledgements

The first author acknowledges the financial support of the Doctoral Program “Vienna Graduate School on Computational Optimization” funded by Austrian Science Foundation under Project No W1260-N35.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsPayame Noor UniversityTehranIran

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