# Mathematics

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## Minimizing a function multiplied by a constant

Let’s say we have an optimization problem.

$\underset{u}{min}(u-5)^2+1 => u=5$

If we multiply it all by some constant, the result does not change.

$\underset{u}{min} 10*((u-5)^2+1) => \underset{u}{min} 10(u-5)^2+10 => u=5$

## EWMA

Exponentially weighted moving average

S**t = Y1 for t = 1

St* = *α* * *Yt + (1 − α)*S**t − 1 for t > 1