MIST: L0 sparse linear regression with momentum

Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty induces sparsity and the natural choice is the so-called l₀ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.