I will be so thankful if someone can help me to determine
How to minimize the following cost function $C$ based on a squared weight matrix $W$:
$$C = (H^TWH)^{-1}(H^TWDWH)(H^TWH)^{-1},$$
where: $H$ is a known tall full column rank matrix and $D$ is a known squared full rank matrix and $H^T$ means $\mathrm{transpose}(H)$.
Note: I know that one convenient (but not optimized) solution is $W=D^{-1}$, but i need to calculate $\frac{dC}{dW}=0$ to have the optimized solution of $W$ as a function of both $H$ and $D$.
Thank you in advance ...