论文部分内容阅读
In this talk,we propose a primal dual active set algorithm(PDAS)for solving a class(both convex and nonconvex)of sparse promoted penalized least square problems in high-dimensional linear regression and compressive sensing.PDAS is derived from a necessary and sufficient condition for coordinate minimizers.DP,MDP and BIC are used to select the regularization parameters automatically during the continuation process(PDASC).We prove local one step convergence of PDAS for the Lasso,and under certain regularity conditions we show that PDASC enjoys sharp statistical error bound and finite steps sign consistency with high probability.For nonconvex models,we establish PDASC is an iterative regularization scheme.Comprehensive simulation studies support our theoretical analysis results and indicate that PDASC is a fast stable and adaptive algorithm that outperforms the state-of-the-art algorithms in terms of efficiency and accuracy.