Abstract
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 B-derivative 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.
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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 DDM-8721709.
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Qi, L., Sun, J. A nonsmooth version of Newton's method. Mathematical Programming 58, 353–367 (1993). https://doi.org/10.1007/BF01581275
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DOI: https://doi.org/10.1007/BF01581275