ADMM Algorithm for Graphical Lasso with an $\ell_{\infty}$ Element-wise Norm Constraint
This work addresses a high-dimensional covariance decomposition problem, but it appears incremental as it builds on existing methods with a specific constraint.
The authors tackled the problem of Graphical Lasso with an additional ℓ∞ element-wise norm constraint on the precision matrix, proposing an ADMM algorithm with a continuation strategy for faster implementation.
We consider the problem of Graphical lasso with an additional $\ell_{\infty}$ element-wise norm constraint on the precision matrix. This problem has applications in high-dimensional covariance decomposition such as in \citep{Janzamin-12}. We propose an ADMM algorithm to solve this problem. We also use a continuation strategy on the penalty parameter to have a fast implemenation of the algorithm.