DCA based approaches for bi-level variable selection and application for estimate multiple sparse covariance matrices

•Two new models via new regularizations for bi-level variable selection are considered.•The first uses the mixed zero norm and the second is the combined ℓ0+ℓq,0 norm.•All the resulting optimization problems are formulated as DC programs.•DCA are investigated via suitable DC decompositions for these DC programs.•The algorithms are applied on estimation of multiple sparse covariance matrices.A careful empirical experiment on both simulated and real datasets are performed.