LaTeX 书写 argmax and argmin 公式

1. arg max or argmax

For a real-valued function $f$ with domain $S$, $\underset{x\in S}{\arg \max f(x)}$ is the set of elements in $S$ that achieve the global maximum in $S$,

{ \underset{x\in S}{{\arg\max} \, f(x)} = \{x \in S: \, f(x) = \max_{y \in S} f(y)\}. }

arg ⁡ max ⁡ f ( x ) x ∈ S = { x ∈ S : f ( x ) = max ⁡ y ∈ S f ( y ) } . { \underset{x\in S}{{\arg\max} \, f(x)} = \{x \in S: \, f(x) = \max_{y \in S} f(y)\}. } x∈Sargmaxf(x)​={x∈S:f(x)=y∈Smax​f(y)}.

For example, if $f(x)$ is $1-|x|$, then $f$ attains its maximum value of $1$ only at the point $x=0$. Thus

$$
{ \underset {x} { \operatorname {arg\,max} } \, (1-|x|) = \{ 0 \}. } 
$$

arg max ⁡ x ( 1 − ∣ x ∣ ) = { 0 } . { \underset {x} { \operatorname {arg\,max} } \, (1-|x|) = \{ 0 \}. } xargmax​(1−∣x∣)={0}.

maxima ['mæksəmə]：n. 最大数，极大值，最大限度，极限，顶点，最高 (maximum 的复数)
maximum [ˈmæksɪməm]：n. 极大，最大限度，最大量 adj. 最高的，最多的，最大极限的

2. arg min or argmin

For a real-valued function $f$ with domain $S$, $\underset{x\in S}{\arg \min f(x)}$ is the set of elements in $S$ that achieve the global minimum in $S$,

$$
{ \underset{x \in S}{{\arg\min} \, f(x)} = \{x \in S: \, f(x) = \min_{y \in S} f(y)\}. }
$$

arg ⁡ min ⁡ f ( x ) x ∈ S = { x ∈ S : f ( x ) = min ⁡ y ∈ S f ( y ) } . { \underset{x \in S}{{\arg\min} \, f(x)} = \{x \in S: \, f(x) = \min_{y \in S} f(y)\}. } x∈Sargminf(x)​={x∈S:f(x)=y∈Smin​f(y)}.

The notion of argmin or arg min, which stands for argument of the minimum, is defined analogously. For instance,

{ \underset {x \in S}{\operatorname {arg\,min} \, f(x)} := \{x \in S ~:~ f(s) \geq f(x){\text{ for all }} s \in S\} }

arg min ⁡ f ( x ) x ∈ S : = { x ∈ S : f ( s ) ≥ f ( x ) for all  s ∈ S } { \underset {x \in S}{\operatorname {arg\,min} \, f(x)} := \{x \in S ~:~ f(s) \geq f(x){\text{ for all }} s \in S\} } x∈Sargminf(x)​:={x∈S : f(s)≥f(x) for all s∈S}

are points $x$ for which $f(x)$ attains its smallest value. It is the complementary operator of arg max.

analogously [ə'næləgəsli]：adv. 类似地，近似地
attain [əˈteɪn]：vt. 达到，实现，获得，到达 vi. 达到，获得，到达 n. 成就

3. Example

$$
\mathcal{G} = \mathop{\text{max}}\limits_{\mathcal{G}} \ \mathcal{U}(\mathcal{G(s)}) \ \text{subject to} \ \text{l}_{r}(\mathcal{G(s)}) = 1, \ \forall s \in S. \tag{1}
$$

$$\mathcal{G}=\underset{\mathcal{G}}{\max }\mathcal{U}(\mathcal{G}(s))\text{subject to}{\text{l}}_r(\mathcal{G}(s))=1,\forall s\in S.\text{\hspace{1em}(1)}$$

4. Wikipedia 中复制 LaTeX 公式

https://en.wikipedia.org/wiki/Arg_max

1. [ edit ]

2. You can view and copy the source of this page:

$$
\underset{x}{\operatorname{arg\,max}}\, (1 - |x|) = \{ 0 \}.
$$

arg max ⁡ x ( 1 − ∣ x ∣ ) = { 0 } . \underset{x}{\operatorname{arg\,max}}\, (1 - |x|) = \{ 0 \}. xargmax​(1−∣x∣)={0}.

References

https://yongqiang.blog.csdn.net/
https://planetmath.org/argminandargmax
https://en.wikipedia.org/wiki/Arg_max