2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131194Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight conditional independence relationships between the sample variables. We first formulate a convex relaxation of this combinatorial problem, we then detail two efficient first-order algorithms with low memory requirements to solve large-scale, dense problem instances.Optimization and ControlStatistics Theory90C22, 62H20, 90C59text