Speaker:Pro Xiaoqi Yang（The Hong Kong Polytechnic University）

Title: Group Sparse Optimization via L_{p,q} Regularization

Time: Thue, Jul.11 2019, AM:9:00-10:00

Location: Room 4318, Building No.4, Wushan Campus

Abstract:

  In this paper, we investigate a group sparse optimization problem via L_{p;q}  regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish an oracle property and a global recovery bound for any point in a level set of the L_{p;q} regularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the L_{p;q} regularization problems, either by analytically solving some specific L_{p;q} regularization subproblems, or by using the Newton method to solve general L_{p;q} regularization subproblems. In particular, we establish a local linear convergence rate of the proximal gradient method for solving the L_{1;q} regularization problem under some mild conditions and by first proving a second-order growth condition. As a consequence, the local linear convergence rate of proximal gradient method for solving the usual L_q regularization problem (0 < q <  1) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.