symmetric quasi-minimum residual iteration

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

Published: 2010/02/20, Updated: 2010/11/17

Convex Optimization, Semi-definite Programming, Statistics inexact search direction, infeasible interior-point method, log-determinant semidefinite programming, sparse inverse covariance selection, symmetric quasi-minimum residual iteration

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

Published: 2005/03/11, Updated: 2005/12/28

Michael J. Todd

Kim-Chuan Toh

Reha H. Tütüncü

Semi-definite Programming nesterov-todd scaling, path-following methods, semidefinite least squares, semidefinite programming, symmetric quasi-minimum residual iteration

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