Assume that we have a weight matrix $W \in \Re^{n x n}$ somewhere and if it's changing, then a vector $J \in \Re^{m}$ is going to be minimized.
The problem is that this is not an ordinary optimization problem such as
$$J = W^Tx$$
Or
$$J = x^TWx$$
It's more like a big model where somewhere inside the model, there are a "tuning parameter", called the weight matrix $W$ and it's affecting the output $J$.
I don't know if it's possible to find a way to optimize $W$ with respect on $J$.
Question:
If you had an algorithm that contains a weight matrix $W$ and it's affecting the output vector $J$. When the sum of $J$ is small, then $W$ and all other parameters are optimal. But how can this be done? Assume that all othe parameters are constants and only $W$ can be changed to minimize the sum of $J$ vector.
How can that be done?