Fast algorithms to solve the Dantzig selector

Abstract

The Dantzig selector is a linear regression model which aims to sparsely represent a response vector by regressors. This paper introduces two fast algorithms which solve the Dantzig selector. One algorithm is linearized alternating direction method (LADMM) which utilizes the separable structure to solve the Dantzig selector; another is a variant of Dantzig selector with sequential optimization (DASSO) which utilizes the sparsity prior to solve the Dantzig selector. We numerically compare the two algorithms on standard data sets, and show that taking advantage of properties of the problem itself enables designing fast algorithms.