, Volume 58, Issue 1-3, pp 353-367

A nonsmooth version of Newton's method

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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.

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.