Dear Marina,
Ignoring the big-O notation for a moment, the first derivative is equal to
. Setting this to zero and solving for
, you obtain the optimal choice for
(as I explained above, the first order optimality condition holds even though the function is strictly speaking not convex).
Best,
Thomas
Ignoring the big-O notation for a moment, the first derivative is equal to
![\frac{1}{2}\sqrt{ \frac{k n \log(n)} {m} } - \frac{n}{m^2} \frac{1}{2}\sqrt{ \frac{k n \log(n)} {m} } - \frac{n}{m^2}](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/fa1d4a4cb63b907b45cb0be70ce343bb.gif)
![m m](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/6f8f57715090da2632453988d9a1501b.gif)
![m m](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/6f8f57715090da2632453988d9a1501b.gif)
Best,
Thomas