Use Newton's method and coordinate descent to solve the regularized inverse covariance matrix estimation problem. Please refer to: Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation, Cho-Jui Hsieh, Matyas A. Sustik, Inderjit S. Dhillon, Pradeep Ravikumar, Advances in Neural Information Processing Systems 24, 2011, p. 2330--2338.