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A trust-region method with improved adaptive radius for systems of nonlinear equations

Author

Listed:
  • Hamid Esmaeili

    (Bu-Ali Sina University)

  • Morteza Kimiaei

    (Islamic Azad University)

Abstract

In this study, a new adaptive trust-region strategy is presented to solve nonlinear systems. More specifically, we propose a new method leading to produce a smaller trust-region radius close to the optimizer and a larger trust-region radius far away from the optimizer. Accordingly, it can lead to a smaller step-size close to the optimizer and a larger one far away from the optimizer. The new strategy includes a convex combination of the maximum norm of function value of some preceding successful iterates and the current norm of function value. The global convergence of the proposed approach is established while the local q-quadratic convergence rate is proved under local error bound condition, which is weaker than the nonsingularity. Numerical results of the proposed algorithm are also reported.

Suggested Citation

  • Hamid Esmaeili & Morteza Kimiaei, 2016. "A trust-region method with improved adaptive radius for systems of nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 109-125, February.
    • Handle: RePEc:spr:mathme:v:83:y:2016:i:1:d:10.1007_s00186-015-0522-0
    DOI: 10.1007/s00186-015-0522-0
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    References listed on IDEAS

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    1. Ju-liang Zhang & Yong Wang, 2003. "A new trust region method for nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 283-298, November.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, September.
    3. Jinyan Fan & Jianyu Pan, 2011. "An improved trust region algorithm for nonlinear equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 59-70, January.
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    Cited by:

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    2. Morteza Kimiaei & Farzad Rahpeymaii, 2019. "A new nonmonotone line-search trust-region approach for nonlinear systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 199-232, July.

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