  We propose a novel quasi-Newton method for solving the sparse inverse
covariance estimation problem also known as the graphical least absolute
shrinkage and selection operator (GLASSO). This problem is often solved using a
second-order quadratic approximation. However, in such algorithms the Hessian
term is complex and computationally expensive to handle. Therefore, our method
uses the inverse of the Hessian as a preconditioner to simplify and approximate
the quadratic element at the cost of a more complex \(\ell_1\) element. The
variables of the resulting preconditioned problem are coupled only by the
\(\ell_1\) sub-derivative of each other, which can be guessed with minimal cost
using the gradient itself, allowing the algorithm to be parallelized and
implemented efficiently on GPU hardware accelerators. Numerical results on
synthetic and real data demonstrate that our method is competitive with other
state-of-the-art approaches.
