New nonsmooth equations-based algorithms for ℓ1-norm minimization and applications

Recently,xiao et al. proposed a nonsmooth equations-based method to solve the ℓ 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 ℓ 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. © 2012 lei wu and zhe sun.