Alternating direction method for covariance selection models

The covariance selection problem captures many applications in various fields, and it has been well studied in the literature. Recently, an l ₁-norm penalized log-likelihood model has been developed for the covariance selection problem, and this novel model is capable of completing the model selection and parameter estimation simultaneously. With the rapidly increasing magnitude of data, it is urged to consider efficient numerical algorithms for large-scale cases of the l₁-norm penalized log-likelihood model. For this purpose, this paper develops the alternating direction method (ADM). Some preliminary numerical results show that the ADM approach is very efficient for large-scale cases of the l₁-norm penalized log-likelihood model.