Editing Newton's method in optimization (section)

{{short description|Method for finding stationary points of a function}}
[[Image:Newton optimization vs grad descent.svg|right|thumb|A comparison of [[gradient descent]] (green) and Newton's method (red) for minimizing a function (with small step sizes). Newton's method uses [[curvature]] information (i.e. the second derivative) to take a more direct route.]] 
<!--__NOTOC__-->

In [[calculus]], '''[[Newton's method]]''' (also called '''Newton–Raphson''') is an [[iterative method]] for finding the [[Zero of a function|roots]] of a [[differentiable function]] <math>f</math>, which are solutions to the [[equation]] <math>f(x)=0</math>. However, to optimize a twice-differentiable <math>f</math>, our goal is to find the roots of <math>f'</math>. We can therefore use Newton's method on its [[derivative]] <math>f'</math> to find solutions to <math>f'(x)=0</math>, also known as the [[Critical point (mathematics)|critical points]] of <math>f</math>. These solutions may be minima, maxima, or saddle points; see section [[Critical point (mathematics)#Several variables|"Several variables"]] in [[Critical point (mathematics)]] and also section [[#Geometric interpretation|"Geometric interpretation"]] in this article. This is relevant in [[Mathematical optimization|optimization]], which aims to find (global) minima of the function <math>f</math>.