my problem is: I want to multiply a bidimensional array of values A by a vector of weights W (A*transpose(W)) but I do not know W but I know the result of the multiplication R, so, I want to estimate the weights W which multiplying A give R as a result.
I suppose it is minimization function by using a langragarian approach The function is
$ \sum_{i=1}^{l}(\sum_{k=1}^{R}a_{ijk}*w_k -v_i) $
with constraints
$\sum_{k=1}^{R}w_k = 1$
and
$w_k \geq 0$, k =0,1,2,.., R
but I do not know how to continue.
Thank you