n
to Rm. Under the assumption of semi-smoothness of the mapping, we prove that the approximation can be obtained through the Clarke generalized Jacobian, Ioffe-Ralph generalized Jacobian, B-subdifferential and their approximations. As an application, we propose a generalized Newton’s method based on the point-based set-valued approximation for solving nonsmooth equations. We show that the proposed method converges locally superlinearly without the assumption of semi-smoothness. Finally we include some well-known generalized Newton’s methods in our method and consolidate the convergence results of these methods.
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Received October 2, 1995 / Revised version received May 5, 1998 Published online October 9, 1998
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Xu, H. Set-valued approximations and Newton’s methods. Math. Program. 84, 401–420 (1999). https://doi.org/10.1007/s101070050028
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DOI: https://doi.org/10.1007/s101070050028