An inexact interior point method for L1-regularized sparse covariance selection

Sparse covariance selection problems can be formulated as log-determinant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual … Read more

Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems

We propose a primal-dual path-following Mehrotra-type predictor-corrector method for solving convex quadratic semidefinite programming (QSDP) problems. For the special case when the quadratic term has the form $\frac{1}{2} X \bul (UXU)$, we compute the search direction at each iteration from the Schur complement equation. We are able to solve the Schur complement equation efficiently via … Read more