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?

  • $\begingroup$ $\argmin f(x)$ is the set of values of $x$ for which $f(x)$ attains its minimum. $\endgroup$ – user122283 May 8 '14 at 4:07
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    $\begingroup$ maybe dup?math.stackexchange.com/questions/227626/explanation-on-arg-min $\endgroup$ – delta May 8 '14 at 4:08
  • $\begingroup$ 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. $\endgroup$ – J. W. Perry May 8 '14 at 4:09
  • $\begingroup$ @J.W.Perry, this notation is used in a research paper in optimization, and it is in english. $\endgroup$ – kou May 8 '14 at 4:11
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    $\begingroup$ My best guess is that you're meant to evaluate over all values of $f(x)$ and $g(y)$, then take the $x$ or $y$ value that gives the smallest result. $\endgroup$ – MartianInvader Dec 4 '14 at 22:55

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