# Notation: what is “arg min”

there is a function that says

$j = \text{argmin}\{ f(x),g(y) \}$

What does that mean?

As noted by the comment, $\text{argmin} f(x)$ is the $x$ that gives smallest $f$. But what happens when $\text{argmin}$ takes two function, what does say?

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$\argmin f(x)$ is the set of values of $x$ for which $f(x)$ attains its minimum. –  Sanath Devalapurkar May 8 '14 at 4:07
–  delta May 8 '14 at 4:08
There is an explanation on arg min in our archives. The answer may be useful to you. What is the language? Just curious. That would indicate how to use the function. –  J. W. Perry May 8 '14 at 4:09
@J.W.Perry, this notation is used in a research paper in optimization, and it is in english. –  kou May 8 '14 at 4:11
I see. It is a mathematical notation and not a programming language snippet. That clarifies things. –  J. W. Perry May 8 '14 at 4:17

This is not correct. $\text{arg}\min f(x)$ is not the minimum value that $f(x)$ attains, but the value of $x$ such that $f(x)$ is minimum. Example: $\text{arg}\min[x^2+1] = 0$ and $\min[x^2+1] = 1$. –  Eff Dec 4 '14 at 22:40