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vault backup: 2024-06-21 06:30:48
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jangyoujin0917 committed Jun 20, 2024
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Expand Up @@ -44,7 +44,7 @@ Assume that global minimum is a only local minimum, and $x'$ is a value that mak
Then, slope of the function $f(x)$ indicates where minimum exists.

- If slope $f'(x_0)$ is positive, it means $x' < x_0$.
- If slope $f'(x_0)$ is positive, it means $x_0 < x'$.
- If slope $f'(x_0)$ is negative, it means $x_0 < x'$.

Therefore, whatever the value of $x_0$ is, $x_1 = x_0 - f'(x_0)$ will move value to the direction of $x'$.
We can do this iteratively, and expect that sequence $\{x_n\}$ will be converge to $x'$.
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