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A new trust region method for nonlinear equations

Author

Listed:
  • Ju-liang Zhang
  • Yong Wang

Abstract

In this paper, a new trust region method for the system of nonlinear equations is presented in which the determining of the trust region radius incorporates the information of its natural residual. The global convergence is obtained under mild conditions. Unlike traditional trust region method, the superlinear convergence of the method is proven under the local error bound condition. This condition is weaker than the nondegeneracy assumption which is necessary for superlinear convergence of traditional trust region method. We also propose an approximate algorithm for the trust region subproblem. Preliminary numerical experiments are reported. Copyright Springer-Verlag 2003

Suggested Citation

  • 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.
  • Handle: RePEc:spr:mathme:v:58:y:2003:i:2:p:283-298
    DOI: 10.1007/s001860300302
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    Citations

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    Cited by:

    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Xianfeng Ding & Quan Qu & Xinyi Wang, 2021. "A modified filter nonmonotone adaptive retrospective trust region method," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-16, June.
    3. 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.
    4. 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.
    5. Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
    6. 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.

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