Optimize matrix arrangement Let's imagine I have a Matrix $\textbf{C}$ whose construction depends on several parameters (and constraints). 
I'm interested in maximizing a value $K$ calculated as:
$K=\frac{-1}{C_{1,1}^{-1}}$
where $C_{1,1}^{-1}$ is the first element of the inverse matrix.
I know that we should never calculate the inverse of a huge matrix. So i can rewrite my problem otherwise but the question will remain the same: is it possible to optimize matrix arrangement corresponding to given constraints to maximize a given value depending on the inverse matrix ? If yes, how ? Is there any theory about it ? 

There is a good chapter in Wilf's book "Mathematical Methods for Digital Computers" p 78. But it is a Monte Carlo approach so therefore it has limited accuracy.
They talk about it here:
https://mathoverflow.net/questions/61813/how-to-find-one-column-or-one-entry-of-the-matrix-inversion
