| Abstract | In this paper, we investigate the theoretical properties and design an efficient numerical algorithm for the .p;q regularization of group sparse optimization. We introduce the group restricted eigenvalue condition, and apply it to establish the oracle result and recovery bound for the .p;q regularization problem. We also apply the proximal gradient method to solve the .p;q regularization problem and obtain analytical formulae for some specific .p;q regularizations. Finally, we present some numerical results on both simulated data and real data in gene transcriptional regulation to demonstrate the performance of the proposed algorithm. |
