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A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations

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  • Yong Li
  • Gonglin Yuan
  • Zengxin Wei

Abstract

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.

Suggested Citation

  • Yong Li & Gonglin Yuan & Zengxin Wei, 2015. "A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-13, May.
    • Handle: RePEc:plo:pone00:0120993
    DOI: 10.1371/journal.pone.0120993
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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. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
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