I've the following system of equations for studying information flow in the below graph,

$\frac{d \phi}{dt}$ = $-M^TDM$ $ \phi$
M is the incidence matrix

$\phi$ is a vector with properties [ A B C D E F]

and I want to determine the value of diagonal elements in the matrix D. The entries in the diagonal elements are the edge weights.

The data that I have is the time-series values of the property $\phi$ at every node. i.e time-series values of A,B,C,D,E,F are available

I'd like to know if there is a way to solve this as an optimization problem using fmincon in Mathematica.

Any suggestions will be really helpful