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In this paper we propose an augmented smoothing function for nonlinear L1-norm minimization problem and consider a global stability of a gradient-basedneural network model to minimize the smoothing function. The numericalsimulations show that our smoothing neural network finds successfully theglobal solution of the L1 -norm minimization problems considered in thesimulation.

An Augmented Smoothing Method of L1 -norm Minimization and Its Implementation by Neural Network Model