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A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations

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Abstract

This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported.

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Authors and Affiliations

  1. Department of Applied Mathematics, Hainan University, Haikou, 570228, Hainan, P. R. China

    Ou Yigui

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  1. Ou Yigui
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Additional information

This work is supported by the Natural Science Foundation of Hainan Province (Grant No. 80552).

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Yigui, O. A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations. J. Appl. Math. Comput. 22, 371–380 (2006). https://doi.org/10.1007/BF02832062

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  • DOI: https://doi.org/10.1007/BF02832062

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