A Unified Primal Dual Active Set Algorithm for Nonconvex Sparse Recovery

In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop novel algorithm primal-dual active set type for class nonconvex sparsity-promoting penalties, including ℓ0, bridge, smoothly clipped absolute deviation, capped ℓ1 and minimax concavity penalty. First, establish existence global minimizer related optimization problems. Then derive necessary optimality condition using associated thresholding operator. The solutions to system are coordinatewise minimizers, under minor conditions, they also local minimizers. Upon introducing dual variable, can be determined primal variables together. Further, relation lends itself an iterative which at each step involves first updating variable only then explicitly. When combined with continuation strategy regularization parameter, method is shown converge globally underlying regression target certain regularity conditions. Extensive numerical experiments both simulated real data demonstrate its superior performance in terms computational efficiency recovery accuracy compared existing methods.