Newton method

$LaTeX: x' = x - J(x)^{-1} F(x),$
where $LaTeX: \textstyle F:\mathbb{R}^n \to \mathbb{R}^n$ $LaTeX: \textstyle (F \in C^1)$ and $LaTeX: J(x)$ is the jacobian of $LaTeX: F$ (assumed nonsingular). In mathematical programming this is used to find a stationary point, where $LaTeX: F=\nabla f$ and $LaTeX: J=H_f.$ Lacking global convergence, this leads to the modified Newton method, sometimes called the damped Newton method. (See the associated myth, Myth NLP-13 to avoid misconception.)