I have this confusion related to optimization of the log(det(X)) function. I didn't get how it implicitly maintains the constraint of X being positive definite.
For eg if I have a matrix
0 1 2
2 4 5
1 6 7
This matrix is not positive definite. However, its determinant is equal to 7 and log(7) is still ok. So I didn't get how the log barrier prevents X from not being positive definite
here is the paper I am referring to
