Mathematical symbol arg meaning _ Mathematics

Reprint: Http://www.cppblog.com/guijie/archive/2010/12/13/136273.aspx

Argument of the Maximum/minimum

arg max F (x): When f (x) takes the maximum value, the value of X

Arg min f (x): When f (x) takes the minimum value, the value of X

Represents the value of a variable when the target function is taken as the minimum value
From Wikipedia

In mathematics, arg max (or Argmax) stands for the argument of the maximum, which is to say, the set of points of the given Argument for which the value of the given expression attains its maximum value:[note 1]

In the other words,

Is the set of values of x for which F (x) has the largest value M. For example, if f (x) are 1−|x|, then it attains its maximum value of 1 in x = 0 and only there, so.

Equivalently, if M is the maximum of F, then the ARG max are the level set of the maximum:

If the maximum is reached in a single value, then one refers to the point as the arg max, meaning we define the arg max as A point, not a set of points. So, for example,//Only one value for the function to take the maximum value, then ARG is the value

(rather than the singleton set {5}), since the maximum value of x (10−X) is, which happens when x = 5. [Note 2]

However, in-case the maximum are reached at many values, arg max is a set of points.

Then, we have for example///If multiple values make the function maximum, ARG is a collection

Since the maximum value of cos (x) is 1, which happens on this interval when x = 0, 2πor 4π. On the "whole real line", the ARG max is

Arg min (or argmin) is defined analogously.

Note also that functions does not in general attain a maximum value, and hence would in general not have a arg max:is unde Fined, as X is unbounded on the real line.  However, by the extreme value theorem (or the classical compactness argument), a continuous function on a compact interval                  Has a maximum, and thus an ARG max. If the maximum value cannot be fetched, no definition