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A nonsmooth version of Newton's method
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Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the Bderivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC ^{2}nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.
This author's work is supported in part by the Australian Research Council.
This author's work is supported in part by the National Science Foundation under grant DDM8721709.
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 Title
 A nonsmooth version of Newton's method
 Journal

Mathematical Programming
Volume 58, Issue 13 , pp 353367
 Cover Date
 19930101
 DOI
 10.1007/BF01581275
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Newton's methods
 generalized Jacobian
 semismoothness
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