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A proximal point algorithm for log-determinant optimization with group Lasso regularization. (English) Zbl 1285.65037
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.

MSC:
65K05 Numerical mathematical programming methods
90C15 Stochastic programming
90C53 Methods of quasi-Newton type
Software:
LMaFit; RecPF
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