ArgMin 2004-07-07 22:39:15 2007-07-02 22:42:43 Definition argmin argmax % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} %\usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here 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 $S$, \[ {\arg \max}_{x \in S} f(x) = \{ x \in S :\, f(x) = \max_{y\in S} f(y) \}. \]