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Zbl 0780.90090
Qi, Liqun; Sun, Jie
A nonsmooth version of Newton's method. (English)
[J] Math. Program. 58, No.3 (A), 353-367 (1993). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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 $C\sp 2$-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.

MSC 2000:: *90C30 Nonlinear programming
49J52 Nonsmooth analysis (other weak concepts of optimality)
49M15 Methods of Newton-Raphson, Galerkin and Ritz types
90-08 Computational methods (optimization)

Keywords: nonlinear equation of several variables; generalized Jacobian; B- derivative; semismoothness; gradient function; augmented Lagrangian

Cited in: Zbl 1236.90146 Zbl 0970.65009 Zbl 0928.65060 Zbl 0838.65054

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