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A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations

Author

Listed:
  • Keyvan Amini

    (Razi University)

  • Mushtak A. K. Shiker

    (Razi University
    University of Babylon)

  • Morteza Kimiaei

    (Islamic Azad University)

Abstract

In this paper, a trust-region procedure is proposed for the solution of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the required number subproblems that must be solved. The global convergence and the local Q-quadratic convergence rate of the proposed approach are proved. Preliminary numerical results of the proposed algorithm are also reported which indicate the promising behavior of the new procedure for solving the nonlinear system.

Suggested Citation

  • Keyvan Amini & Mushtak A. K. Shiker & Morteza Kimiaei, 2016. "A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations," 4OR, Springer, vol. 14(2), pages 133-152, June.
    • Handle: RePEc:spr:aqjoor:v:14:y:2016:i:2:d:10.1007_s10288-016-0305-3
    DOI: 10.1007/s10288-016-0305-3
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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.
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    Cited by:

    1. 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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