I've got to solve an optimisation problem and don't know how to approach this (I'm thinking of writing a script to solve the problem recursively but wonder if there's another approach).
The target is given by $n$ real numbers, e. g. $a_{1t} = 10$, $a_{2t} = 20$, $a_{3t}=30$.
I've got the current value of the $n$ numbers, e. g. $a_{11}=1$, $a_{21}=1$, $a_{31}=5$.
I can change these numbers as follows:
a_{12} = a_{11} + \eta · \mu_1
a_{22} = a_{21} + \eta · \mu_2
a_{32} = a_{31} + \eta · \mu_3
I need to find $\eta$ so that the mean square root between the two sequences is minimal when changing the $n$ numbers according to this rules where $\mu_1$, $\mu_2$ and $\mu_3$ are fixed factors (e. g. $1$, $2$ and $3$).