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 C2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.
| Original language | English |
|---|---|
| Pages (from-to) | 353-367 |
| Number of pages | 15 |
| Journal | Mathematical Programming |
| Volume | 58 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - 1 Jan 1993 |
| Externally published | Yes |
Keywords
- generalized Jacobian
- Newton's methods
- semismoothness
ASJC Scopus subject areas
- Software
- General Mathematics
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