LaTeX 书写 argmax and argmin 公式 |
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LaTeX 书写 argmax and argmin 公式
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LaTeX 书写 argmax and argmin 公式
1. `arg max` or `argmax`2. `arg min` or `argmin`3. Example4. Wikipedia 中复制 LaTeX 公式References
1. arg max or argmax
For a real-valued function f f f with domain S S S, arg max f ( x ) x ∈ S \underset{x\in S}{{\arg\max} \, f(x)} x∈Sargmaxf(x) is the set of elements in S S S that achieve the global maximum in S S 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∈Smaxf(y)}. For example, if f ( x ) f(x) f(x) is 1 − ∣ x ∣ 1-|x| 1−∣x∣, then f f f attains its maximum value of 1 1 1 only at the point x = 0 x=0 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 argminFor a real-valued function f f f with domain S S S, arg min f ( x ) x ∈ S \underset{x \in S}{{\arg\min} f(x)} x∈Sargminf(x) is the set of elements in S S S that achieve the global minimum in S S 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∈Sminf(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 x x for which f ( x ) f(x) 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 $$ \mathcal{G} = \mathop{\text{max}}\limits_{\mathcal{G}} \ \mathcal{U}(\mathcal{G(s)}) \ \text{subject to} \ \text{l}_{r}(\mathcal{G(s)}) = 1, \ \forall s \in S. \tag{1} $$G = max G U ( G ( s ) ) subject to l r ( G ( s ) ) = 1 , ∀ s ∈ S . (1) \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} G=Gmax U(G(s)) subject to lr(G(s))=1, ∀s∈S.(1) 4. Wikipedia 中复制 LaTeX 公式https://en.wikipedia.org/wiki/Arg_max [ edit ]
arg max x ( 1 − ∣ x ∣ ) = { 0 } . \underset{x}{\operatorname{arg\,max}}\, (1 - |x|) = \{ 0 \}. xargmax(1−∣x∣)={0}. References[1] Yongqiang Cheng, https://yongqiang.blog.csdn.net/ https://planetmath.org/argminandargmax https://en.wikipedia.org/wiki/Arg_max |
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