Talk:Maximum and minimum

message: Comparing with mathworld's definition , I wonder if our definition could be too informal. Mathworld says: "A global maximum of a function  is the largest value in the entire range  of the function, and a local maximum is the largest value in some local neighborhood." Are we confusing the maximum with the point in the domain where the function takes such a maximum? Can anyone clarify this, please? Another Wikipedian 04:00, 12 May 2007 (UTC)
thread_title:  Do minima and maxima belong to the range or to the domain? 

message: The problem is how sophisticated to make this discussion. OK, explain everything at first in terms as simple as possible, and only for functions from "all reals" to reals. BUT for such functions it is true that every global extremum is also a local extremum; and it needs to be explained that such an assumption is not universal - especially for optimization problems (a couple of paragraphs down) on a finite domain where the possibilities to be considered are (1) global extrema at endpoints of closed intervals of the domain, and (2) local extrema at interior points. So, after introducing the simple case where the domain is "all reals" and global extrema are always local extrema, it is NECESSARY to point out that the definition of local (but not global) extrema involves some kind of "neighborhood" concept which does not apply at the endpoints of finite portions of the domain. And it follows that on some kinds of restricted domains it is NOT TRUE that global extrema are always local extrema, in particular when they occur at endpoints. L P Meissner 03:51, 20 May 2007 (UTC)
thread_title:  Local max/min when domain is restricted 

message: http://pl.wikipedia.org/wiki/Ekstremum is so much better than ours..
Miserlou (talk) 16:47, 3 March 2008 (UTC)
thread_title:  Anybody speak Polish? 

message: I'm curious about algorithms to find global extrema. I think there is theory out there about it such as use of scale space for optical flow problems. I did some Googling and found this short discussion, along with other hits. Can anyone point me to other ways of searching for global extrema in an efficient way when there are many local extrema? —Ben FrantzDale (talk) 02:02, 28 May 2008 (UTC)
thread_title:  Finding global extrema 

message: The graph currently at the head of the page is incorrect in indicating that the right-most point of the curve is a local maximum (cf. body text).  I have students who are confused on precisely this point and would like to set it right, but I don't know how to deal with images on Wikipedia.  Perhaps someone with a little more nous could correct this blatant error?  Wooster (talk) 14:38, 1 January 2009 (UTC)
thread_title:  Incorrect graph 

message: There is more than 2 local extremas in this picture, 5 exactly.  —Preceding unsigned comment added by 81.219.148.7 (talk) 20:27, 16 September 2009 (UTC)
thread_title: Problem with image

message: It seems to me that we don't need a function to be real-valued in order to talk about absolute maxima and minima---all we need is that the range have some sort of partial order.
In addition, if the domain of the function has a topology, we have enough notion of locality to talk about local maxima and minima.
This isn't exactly an earth-shattering observation, but it does seem like it would fit in the article. Unfortunately it's "original research" until I can source it. Is anyone familiar with a published definition along these lines? If not, is there any easy way to turn it into something I can put on Wikipedia? --Ian Maxwell (talk) 14:59, 3 April 2009 (UTC)
thread_title:  Sourcing for an original claim 

message: Regarding the example:
"The function cos(x) has infinitely many global maxima at 0, ±2π, ±4π, …, and infinitely many global minima at ±π, ±3π, …."
In my opinion this should read correctly:
The function cos has one global maximum (i.e. 1) at infinitely many points x = 0, ±2π, ±4π, …, and one global minimum (i.e. -1) at infinitely many points x = ±π, ±3π, ….
--84.74.161.179 (talk) 03:40, 4 May 2013 (UTC)
thread_title:  Number of Global Maxima/Minima of cos 

message: When is this possible (or not possible)? I think this article needs clarification. I see a lot of elementary calculus textbooks claiming that it is not possible for a global maximum to have a value of infinity, but then again, the topology definition in this article seems to permit x* to take on a value of infinity.  — Preceding unsigned comment added by 67.165.41.60 (talk) 04:26, 17 October 2013 (UTC)
thread_title:  Infinity as a maximum value? 

message: The definitions are slightly different, as the arg max is a component of the global maximum point(s), but Arg max mostly duplicates the definitions laid out here, and it would be very hard to expand the arg max article without further duplicating information which also belongs in maxima and minima. Forbes72 (talk) 05:06, 3 April 2015 (UTC)
thread_title: Merge with Arg max

message: I think this article and two comments beneath it (http://grammarist.com/usage/maxima-maximums ) make a valid case on which is used more regularly and in which context: Maximums/Minimums are the usual (in America and beyond now) in more general parlance, while Maxima/Minima are still commonplace in more mathematical/scientific usages. As per the comments, testing the word Maxima can give skewed answers, as it's also used as a word form for Maximus, hence search engines do not give accurate results on the most used over Maximums. The article should surely reflect both these issues; I just added the -ums to the -a as being noted plurals, although the  Maximus adjective usage is not commented upon in the article yet, so a "Miscellanious" or perhaps "Terminology" section point of note to readers could be added in addition. Jimthing (talk) 16:22, 6 April 2015 (UTC)
thread_title:  Maximums vs Maxima / Minimums vs Minima 

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thread_title:  External links modified