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Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the ℓ1-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 ℓ1-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.

New Nonsmooth Equations-Based Algorithms for ℓ1-Norm Minimization and Applications