Algorithm 3 DP-GLASSO algorithm

Initialize Θ = diag(S + λI)−1. Cycle around the columns repeatedly, performing the following steps till convergence: Rearrange the rows/columns so that the target column is last (implicitly). Solve (5.3) for $\tilde{\mathbf{\gamma }}$ and update $${\widehat{\mathit{\theta }}}_{12}=-{\mathbf{\Theta }}_{11}({\mathbf{s}}_{12}+\tilde{\mathbf{\gamma }})/w_{22}$$ Solve for θ22 using (5.5). Update the working covariance ${\mathbf{w}}_{12}={\mathbf{s}}_{12}+\tilde{\mathbf{\gamma }}$.