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Newton Methods for Solving Two Classes of Nonsmooth Equations

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Abstract

The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not require an element of Clarke generalized Jacobian, of B-differential, or of b-differential, at each iteration point.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, China University of Mining and Technology, Beijing, 100083, China

    Yan Gao

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  1. Yan Gao
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Gao, Y. Newton Methods for Solving Two Classes of Nonsmooth Equations. Applications of Mathematics 46, 215–229 (2001). https://doi.org/10.1023/A:1013791923957

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  • DOI: https://doi.org/10.1023/A:1013791923957

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