New nonsmooth equations-based algorithms for \(\ell_1\)-norm minimization and applications (Q1952757)

Summary: Recently, \textit{Y. Xiao} et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 11, 3570--3577 (2011; Zbl 1217.65069)] proposed a nonsmooth equations-based method to solve the \(\ell_1\)-norm minimization problem. 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.