A Smoothing Newton Method For Finding A Minimizing E₁-norm Solution To A Linear Sys-tem Of Equations

This paper focus on a type of mathematical programs with l1-norm objective func-tion. With the help of the square smoothing function.We constract a smoothing approx-imation of the mathematical programs with l1-norm objective function.The smoothing Newton method and inexact smoothing Newton method ace employed to solve the per-turbed problem.The global convergence and local quadratic convergence of the smoothing Newton method and inexact smoothing Newton method are showm.Finally,the numerical results of the two methods are reported and compared.1,In Chapter 2. We reviews the preliminanaries and preliminary results on the background in nonsmooth analysis which will be used in the following passage.2,In chapter 3. We constract a smoothing approximation of the orignal problem with the help of the square smoothing function.3,We employ the Smoothing Newton method to solve the perturbed problem and demonstrate the global convergence and local quadratic convergence rate.The numerical results of smoothing Newton method are reported in Chapter 4.4,We employ the inexact Smoothing Newton method to solve the perturbed prob-lem and demonstrate the global convergence and local quadratic convergence rate.The numerical results of smoothing Newton method are reported in Chapter 5.