# 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 for*C*^{2}-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.

## Key words

Newton's methods generalized Jacobian semismoothness## Preview

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© The Mathematical Programming Society, Inc. 1993