Exponential Mixture Density,cannot calculte inverse matrix

I am trying to find the solution of Exponential Mixture density, which is to estimate covariance and mean of a new Gaussian distribution from data fusion of several Gaussian distributions. Suppose I have A, B and a, b, which are covariance and mean of two Gaussian. The new covariance C and mean c is given by:
minimize (D1-D2)^2
s.t. omig1+omig2=1
Where D1 and D2 is KL divergence.
Since inv cannot be used, I just omig1
inv(A) into omig1/A.However this doesn’t work for C:
It says divider matrix must be constant.So how can I generate inverse matrix over here.

Are you sure your formulation is convex? If so, how dd you prove that?

actually covariance intersection (algorithm to get C and c)is proved to be convex in a lot of materials. I’m not sure if the minimization of KL divergence is also convex, but before that how to obtain C, which should be convex through inverse operation.