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arg min and arg max
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(Definition)
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For a real-valued function $f$ with domain $S$ $\arg \min_{x \in S} f(x)$ is the set of elements in $S$ that achieve the global minimum in $S$ $$ {\arg \min}_{x \in S} f(x) = \{ x \in S :\, f(x) = \min_{y\in S} f(y) \}. $$
$\arg \max_{x \in S} f(x)$ is the set of elements in $S$ that achieve the global maximum in $S$ $$ {\arg \max}_{x \in S} f(x) = \{ x \in S :\, f(x) = \max_{y\in S} f(y) \}. $$
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"arg min and arg max" is owned by kshum.
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(view preamble | get metadata)
| Also defines: |
argmin argmax |
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Cross-references: global maximum, global minimum, domain, function
This is version 8 of arg min and arg max, born on 2004-07-07, modified 2007-07-02.
Object id is 5986, canonical name is ArgMin.
Accessed 19164 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) |
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Pending Errata and Addenda
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