Yang, Junfeng; Sun, Defeng; Toh, Kim-Chuan A proximal point algorithm for log-determinant optimization with group Lasso regularization. (English) Zbl 1285.65037 SIAM J. Optim. 23, No. 2, 857-893 (2013). The authors propose a proximal point algorithm for the solution of covariance selections problems, where it is assumed that the inverse covariance matrix has a block sparsity structure. In each iteration of the optimization algorithm the dual subproblem is used to update the primal variable. This approach is combined with an inexact Newton method to accelerate the optimization process. Global and local convergence results for the proposed method are proved. Furthermore, comprehensive numerical results are presented and discussed. Reviewer: Andrea Walther (Paderborn) Cited in 13 Documents MSC: 65K05 Numerical mathematical programming methods 90C15 Stochastic programming 90C53 Methods of quasi-Newton type Keywords:proximal point algorithm; covariance selection; log-determinant optimization; group Lasso regularization; augmented Lagrangian; alternating direction method; Newton’s method; Gaussian graphical model; convergence; numerical result Software:LMaFit; RecPF PDF BibTeX XML Cite \textit{J. Yang} et al., SIAM J. Optim. 23, No. 2, 857--893 (2013; Zbl 1285.65037) Full Text: DOI