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A parameterized Newton method and a quasi-Newton method for nonsmooth equations

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Abstract

This paper presents a parameterized Newton method using generalized Jacobians and a Broyden-like method for solving nonsmooth equations. The former ensures that the method is well-defined even when the generalized Jacobian is singular. The latter is constructed by using an approximation function which can be formed for nonsmooth equations arising from partial differential equations and nonlinear complementarity problems. The approximation function method generalizes the splitting function method for nonsmooth equations. Locally superlinear convergence results are proved for the two methods. Numerical examples are given to compare the two methods with some other methods.

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Authors and Affiliations

  1. School of Mathematics, University of New South Wales, P.O. Box 1, 2033, Kensington, NSW, Australia

    Xiaojun Chen & Liqun Qi

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  1. Xiaojun Chen
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  2. Liqun Qi
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This work is supported by the Australian Research Council.

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Chen, X., Qi, L. A parameterized Newton method and a quasi-Newton method for nonsmooth equations. Comput Optim Applic 3, 157–179 (1994). https://doi.org/10.1007/BF01300972

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