On proximal gradient method for the convex problems regularized with the group reproducing kernel norm

Authors:
Haibin Zhang;Juan Wei;Meixia Li;Jie Zhou;Miantao Chao
Affiliations:
College of Applied Sciences, Beijing University of Technology, Beijing, China 100124;College of Applied Sciences, Beijing University of Technology, Beijing, China 100124;College of Applied Sciences, Beijing University of Technology, Beijing, China 100124 and School of Mathematics and Information Science, Weifang University, Weifang, China 261061;College of Applied Sciences, Beijing University of Technology, Beijing, China 100124;College of Applied Sciences, Beijing University of Technology, Beijing, China 100124
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping, regularized by the group reproducing kernel norm. This class of problems arise naturally from applications in group Lasso, which is a popular technique for variable selection. An effective approach to solve such problems is by the proximal gradient method. In this paper we derive and study theoretically the efficient algorithms for the class of the convex problems, analyze the convergence of the algorithm and its subalgorithm.