New Nonsmooth Equations-Based Algorithms for ℓ 1 -Norm Minimization and Applications

Abstract

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the ${\ell }_1$-norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving ${\ell }_1$-norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms.