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> but then your starting point is already at the optimum Newton raphson is used to find where f(x) = 0, not where the derivative f'(x) = 0. For the function g
by mijoharas 5y ago
> but then your starting point is already at the optimum
Newton raphson is used to find where f(x) = 0, not where the derivative f'(x) = 0.
For the function given above f(x) = 0 when x = 1 and x = -1. Not when the derivative is at 0 (when x = 0).
You'd be done in 0 steps to find the minimum of the function, or the point of 0 derivative, but that's not what you're looking for with newton raphson.
- abeppu 5y agoNewton's method is _commonly_ used for function minimization by looking for the zero of the derivative, and this is entirely what the article is about. In sec 1.1 at the top of page 2, they say very clearly "In this work, we are interested in solving the unconstrained minimization problem ...". Even in the first para, they say "Newton’s method is a cornerstone of convex optimization", meaning optimization/minimization of a convex function. The article says "Unfortunately, Newton’s method is unstable: it works only for strongly convex problems and may diverge exponentially when initialized not very close to the optimum." And I was asking for an example or description of such a case. You'll also note there are several comments in this discussion that mention the hessian/2nd order derivatives, and these all show up because this is being used in the context of optimization by looking for f'(x) = 0.