What is the sub-topic that deals with this kind of optimization problems?

Question

I am encountering a deluge of optimization problems of the following kind

$$\begin{array}{ll} \text{minimize} & \mbox{tr}(WKLKW)\\ \text{subject to} & WKHKW=I\end{array}$$

where the minimization is over $W$, and everything is a matrix. Almost invariably, the solution ends up being based on the eigendecomposition of some matrix expression. It's like the Rayleigh quotient, but way more complicated.

1. I want to get seasoned in solving these kinds of problems. Where can I find them?

2. What is the broad name for these types of problems? What should I search for?

3. Any links or lectures on them?

Answer 1

It's a joke my friend.

$WK=W^{-1}K^{-1}H^{-1}$. Then we consider $tr(W^{-1}K^{-1}H^{-1}LKW)=tr(K^{-1}H^{-1}LK)=tr(H^{-1}L)$, that is a constant