In this project, we consider the problem of recovering a sparse vector in the context of a linear regression model. We develop an algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, which cover $\ell^0$, bridge, smoothly clipped absolute deviation, capped $\ell^1$ and minimax concavity penalty. The solutions to the optimality system are coordinate-wise minimizers, and under minor conditions, they are also local minimizers. Upon introducing the dual variable, the active set can be determined from the primal and dual variables. This relation lends itself to an iterative algorithm of active set type which at each step involves updating the primal variable only on the active set and then updating the dual variable explicitly. When combined with a continuation strategy on the regularization parameter, the primal dual active set method has a global convergence property under the restricted isometry property. Extensive numerical experiments demonstrate its superior performance in efficiency and accuracy compared with the existing methods.

Installation

To install the development version of PDAS, it's easiest to use the 'devtools' package. Note that PDAS depends on the 'Rcpp' package, which also requires appropriate setting of Rtools and Xcode for Windows and Mac OS/X, respectively.

#install.packages("devtools")
library(devtools)
install_github("gordonliu810822/PDAS")