Abstract.
A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods and inexact-Newton methods for solving the system of nonsmooth equations and for solving the system of equations of smooth compositions of nonsmooth functions, are developed. The Q-superlinear convergence of Newton methods and the Q-linear convergence of inexact-Newton methods are shown. The present Newton methods and inexact-Newton methods could be viewed as the extensions of previous ones with same convergent results.
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Manuscript received: May 2000/Final version received: May 2001
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Gao, Y. Newton methods for solving nonsmooth equations via a new subdifferential. Mathematical Methods of OR 54, 239–257 (2001). https://doi.org/10.1007/s001860100150
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DOI: https://doi.org/10.1007/s001860100150