人大论坛太管用了，搜百度直接搜晕了

1# jinnson

n mathematics, arg max (or argmax) stands for the argument of the maximum, that 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 other words,
is the set of values of x for which f(x) has the largest value M. For example, if f(x) is 1?|x|, then it attains its maximum value of 1 at x = 0 and only there, so .

Equivalently, if M is the maximum of f, then the arg max is the level set of the maximum:
If the maximum is reached at 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,
(rather than the singleton set {5}), since the maximum value of x(10 ? x) is 25, which happens when x = 5.[note 2]
However, in case the maximum is reached at many values, arg max is a set of points.
Then, we have for example
since the maximum value of cos(x) is 1, which happens on this interval when x = 0, 2π or 4π. On the whole real line, the arg max is
arg min (or argmin) is defined analogously.
Note also that functions do not in general attain a maximum value, and hence will in general not have an arg max: is undefined, as x isunbounded on the real line. However, by the extreme value theorem (or the classical compactness argument), a continuous function on a compact intervalhas a maximum, and thus an arg max.




from :    http://en.wikipedia.org/wiki/Arg_max

学习了，多谢。

论坛真是好地方！

论坛是个好地方~

arguement maximun

论坛确实是个好地方

论坛真是好地方！

t0应该是集合的集合吧？恕我想的不够深刻（我是根据反函数想了想）

赞一个

我觉得用经典、简洁的数学公式，说明argmax比较好，因为它本身就是个数学表达：
请看以下的公示解释：

We describe the problem as maximizing y with respect to x.

If y∗ is the maximum value of f(x) then we write y∗ = max f(x).

If x∗ is the value of x that maximizes f(x) we write x∗ = arg max f(x)

即，x*是使f(x)取最大值的那个值。一般可以用一阶求导取得。

这个argmax 表达，一般用在博弈论的激励约束条件中，
即，使agent（代理人）的效用最大化（同时又符合principle委托人的利益取向）时， 代理人需要付出的努力水平，求解方法，也是直接取一阶导。

受教了