In this talk, we will present a group sparse optimization problem via $\ell_{p,q}$ regularization $(0\le q<1)$ in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we will establish an oracle property and a global recovery bound of order $O(\lambda^\frac{2}{2-q})$ for the $\ell_{p,q}$ regularization problem. In the algorithmic aspect, we will apply the well-known proximal gradient method to solve the $\ell_{p,q}$ regularization problem and establish the linear convergence rate under a simple assumption. Finally, in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.