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A BFGS trust-region method for nonlinear equations

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Abstract

In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic convergence are obtained under suitable conditions. Numerical results show that this method is more effective than the norm method.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, People’s Republic of China

    Gonglin Yuan & Zengxin Wei

  2. School of Science, East China University of Science and Technology, 200237, Shanghai, People’s Republic of China

    Xiwen Lu

Authors
  1. Gonglin Yuan
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  2. Zengxin Wei
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  3. Xiwen Lu
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Corresponding author

Correspondence to Gonglin Yuan.

Additional information

This work is supported by China NSF grands 10761001, the Scientific Research Foundation of Guangxi University (Grant No. X081082), and Guangxi SF grands 0991028.

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Yuan, G., Wei, Z. & Lu, X. A BFGS trust-region method for nonlinear equations. Computing 92, 317–333 (2011). https://doi.org/10.1007/s00607-011-0146-z

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  • DOI: https://doi.org/10.1007/s00607-011-0146-z

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