# arg min and arg max

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

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

$\mathrm{arg}{\mathrm{max}}_{x\in S}f(x)$ is the set of elements in $S$ that achieve the global maximum in $S$,

$$\mathrm{arg}\underset{x\in S}{\mathrm{max}}f(x)=\{x\in S:f(x)=\underset{y\in S}{\mathrm{max}}f(y)\}.$$ |

Title | arg min and arg max |
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Canonical name | ArgMinAndArgMax |

Date of creation | 2013-03-22 14:27:55 |

Last modified on | 2013-03-22 14:27:55 |

Owner | kshum (5987) |

Last modified by | kshum (5987) |

Numerical id | 11 |

Author | kshum (5987) |

Entry type | Definition |

Classification | msc 00A05 |

Defines | argmin argmax |