  We consider estimation of undirected Gaussian graphical models and inverse
covariances in high-dimensional scenarios by penalizing the corresponding
precision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (Graphical
Ridge) penalties for the precision matrix have already been studied, we propose
the combination of both, yielding an Elastic Net type penalty. We enable
additional flexibility by allowing to include diagonal target matrices for the
precision matrix. We generalize existing algorithms for the Graphical Lasso and
provide corresponding software with an efficient implementation to facilitate
usage for practitioners. Our software borrows computationally favorable parts
from a number of existing packages for the Graphical Lasso, leading to an
overall fast(er) implementation and at the same time yielding also much more
methodological flexibility.
