In this talk, we consider a class of nonsmooth convex optimization problems. The class of problems arises naturally from applications in sparse group Lasso etc, which is a popular technique for variable selection. An effective approach to solve such problems is by the proximal gradient method (PGM), one of the proximal splitting methods. We talk about the establishment of the algorithm and the linear convergence of the PGM for the class of problems.
  Joint work with Luo Zhi-Quan and Jiang Jiaojiao.