Feature splitting parallel algorithm for Dantzig selectors

The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets into manageable subsets that can be stored and processed more easily on a single machine. This paper proposes a variable splitting parallel algorithm for solving both convex and nonconvex Dantzig selectors based on the proximal point algorithm. The primary advantage of our parallel algorithm, compared to existing parallel approaches, is the significantly reduced number of iteration variables, which greatly enhances computational efficiency and accelerates the convergence speed of the algorithm. Furthermore, we show that our solution remains unchanged regardless of how the data is partitioned, a property referred to as partitioninsensitive. In theory, we use a concise proof framework to demonstrate that the algorithm exhibits linear convergence. Numerical experiments indicate that our algorithm performs competitively in both parallel and nonparallel environments. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/PPADS.