Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the -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 -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 -Norm Minimization and Applications." J. Appl. Math. 2012 (SI06) 1 - 14, 2012. https://doi.org/10.1155/2012/139609