Abstract: Inferring gene regulatory networks from gene expression data and identifying key factors for cell fate conversion are two arduous challenges in biology and regenerative medicine, especially in higher organisms (like human and mouse) where the number of genes is large but the number of experimental samples is small. In this talk, we will formulate these two systems biology problems into structured sparse optimization problem by employing the special structure of the involved regulatory networks. The lower-order regularization method for structured sparse optimization will be introduced in a unified framework. Theoretical guarantee of the lower-order regularization method is provided via the oracle property and recovery bound, and the numerical performance of the proximal gradient algorithm is presented via the linear convergence property. The applications of group sparse optimization will facilitate biologists to study the gene regulation of higher model organisms in a genome-wide scale.