Newton methods for solving nonsmooth equations via a new subdifferential

Yan Gao

Mathematical Methods of Operations Research, 2001, vol. 54, issue 2, 239-257

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. Copyright Springer-Verlag Berlin Heidelberg 2001

Keywords: Key words: nonsmooth equations; nonsmooth optimization; Newton methods; inexact-Newton methods; semismoothness; composite functions (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/s001860100150

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