Abstract
This paper presents sufficient and necessary conditions for the convergence of Newton’s method based on generalized derivatives. These conditions require uniform injectivity of the derivatives as well as uniform high-order approximation of the original locally Lipschitz function along rays through the solution. Our approach permits to determine approximate solutions of the Newton subproblems and to use such concepts of derivatives for nonsmooth functions, multivalued or not, as directional and B-derivatives, contingent derivatives, generalized Jacobians and others. Furthermore, we ensure solvability of the subproblems via surjecivi-ty of the derivatives and verify a Kantorovich-type convergence theorem.
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Kummer, B. (1992). Newton’s Method Based on Generalized Derivatives for Nonsmooth Functions: Convergence Analysis. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_12
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DOI: https://doi.org/10.1007/978-3-642-51682-5_12
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