Talk:Newton's method in optimization

message: There is another wikipedia page called Newton's method (http://en.wikipedia.org/wiki/Newton%27s_method#Nonlinear_systems_of_equations). I suggest both are merged or the content is just too confusing and even seemingly contradictory.
Alpheratzstar (talk) 12:25, 9 November 2011 (UTC)
replies: text: I think it is good to seperate like this. The point is there are some differences between: solving systems of non-linear equations (the original purpose of Newton's method) and solving optimization problems (this Wikipedia page). For example, in optimization problems, one wants to find local minima, but Newton's method will converge to a saddle point if the initial point is close to that saddle point. Tuyentruongoslo (talk) 05:46, 19 March 2021 (UTC)
thread_title: Should be merged with Newton's method

message: Could someone write a piece on Halley's method in multi-dimensional case?
I could only find this on the German page, and can't really follow it very well: http://de.wikipedia.org/wiki/Halley-Verfahren
I also realize that this is not really the Newton's method, but there are many similarities and more people are likely to visit this page.....   — Preceding unsigned comment added by 90.215.230.136 (talk) 15:34, 22 July 2011 (UTC)
replies: text: I think you are mixing up quasi-NM with the real thing. 018 (talk) 18:55, 18 October 2011 (UTC)
thread_title: Needs more generalization

message: The formula presented is the method applied to find the root of f(x), or to find a minimum, applying the method to f'(x)?? -- NIC1138 17:27, 21 June 2007 (UTC)
replies: text: The second is right, applying the method to f'(x). I think that's mentioned in the intro. Oleg Alexandrov (talk) 01:59, 22 June 2007 (UTC)
thread_title:  Root or minimum?? 

message: I think there is an error in the formala:
\mathbf{p}_{n} = \mathbf{x}_{n+1}-\mathbf{x}_{n} = -[H f(\mathbf{x}_n)]^{-1} \nabla f(\mathbf{x}_n), \ n \ge 0.
I think to make it a linear equation it should be
\mathbf{p}_{n} = [H f(\mathbf{x}_n)] (\mathbf{x}_{n+1}-\mathbf{x}_{n}) = -\nabla f(\mathbf{x}_n), \ n \ge 0.
or perhaps
[H f(\mathbf{x}_n)] \mathbf{p}_{n}  = -\nabla f(\mathbf{x}_n), \ n \ge 0.
with 
\mathbf{x}_{n+1} = \mathbf{p}_{n} + \mathbf{x}_{n}
Any objections?  —Preceding unsigned comment added by 91.19.151.5 (talk) 11:32, 5 October 2007 (UTC)
replies: text: Not sure if I understand what you meant. Can you be clearer? For example, I don't see any error with this: \mathbf{p}_{n} = \mathbf{x}_{n+1}-\mathbf{x}_{n} = -[H f(\mathbf{x}_n)]^{-1} \nabla f(\mathbf{x}_n), \ n \ge 0. Tuyentruongoslo (talk) 05:50, 19 March 2021 (UTC)
thread_title:  Error in the formula? 

message: The below was added by Tuyentruongoslo  to the article.  I'm moving them to here, should anyone wish to address them.  --Escape Orbit (Talk) 12:44, 17 March 2021 (UTC)
replies: text: How can I add one remark in the article that the section needs clarified? Tuyentruongoslo (talk) 22:54, 17 March 2021 (UTC)
thread_title:  Comments 

message: In the introduction : I don't understand why the notation F(x) is switched to f(x) : is it the same function ? Pierre g111 (talk) 04:45, 27 July 2023 (UTC)
thread_title:  ask for a clarification for notations