Smoothing Function for Minimum 1-Norm Linear Equation System

In this paper, we propose a new smoothing function for L1-norm minimization problems where the objective function is not differentiable. Such optimization problems arise from wide applications such as compressed sensing, image restoration, signal reconstruction, etc. that have direct influence on the technology we use every day. For instance, compressed sensing is the process of acquiring and reconstructing a signal that is supposed to be sparse or compressible in electrical engineering, particularly in signal processing. Furthermore, we analyze the properties of the smoothed optimization model to the problem as well as produce a new algorithm for solving it. The global convergence and rate of convergence of the algorithm are also taken into consideration. Although there are numerous algorithms that have been introduced and studied for solving the aforementioned L1-problem, we hope to find a more efficient method for solving a non-smooth optimization problem which results in a minimum 1-norm solution for linear equation system