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Global Convergence
Numerical Method
superlinear convergence
Systems of Nonlinear Equations
Variational Analysis
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Generalized Newton's Method based on Graphical Derivatives
Generalized Newton's Method based on Graphical Derivatives,T. Hoheisel,C. Kanzow,B. S. Mordukhovich,H. Phan
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Generalized Newton's Method based on Graphical Derivatives
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T. Hoheisel
,
C. Kanzow
,
B. S. Mordukhovich
,
H. Phan
This paper concerns developing a
numerical method
of the Newton type to solve
systems of nonlinear equations
described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newtontype method for solving nonsmooth equations. Based on advanced techniques of
variational analysis
and generalized differentiation, we establish the wellposedness of the algorithm, its local superlinear convergence, and its
global convergence
of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with wellrecognized semismooth and $B$differentiable versions of Newton's method for nonsmooth Lipschitzian equations.
Published in 2010.
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