I have a covariance matrix C. I have then formulated an quadratic optimization problem that involves the following matrix in the quadratic form:

[ C C ]

[ C C ]

However, the quadratic solver complains that this matrix is not positive definite. I can also reformulate the optimization problem so that it uses the following matrix in quadratic form:

[ C -C ]

[-C C ]

This matrix is also not positive definite. Now, I know that the problem I am trying to solve might not be possible to set up for quadratic optimization. However, I was wondering if maybe someone encountered a similar setup before, and can give me any hints? Maybe reformulate the problem? Or do some approximation? Make the matrix positive definite somehow? I know, now very clear, but I don't know what else I could add. Thank you!