Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
$\argmin f(x)$ is the set of values of $x$ for which $f(x)$ attains its minimum. – Sanath K. Devalapurkar May 8 '14 at 4:07
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
up vote -2 down vote accepted

As I understand it, arg_min is the minimum value that f(x) and g(y) share. It is used in optimization.

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.