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

Abstract EN

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.