Smoothing Approximations For Non Square Matrix Norm Optimization Problem

Matrix norm optimization problems are the research objects of modern engineer-ing technology. For symmetrical matrices2-norm minimization, we are familiar with interior-point method, augmented Lagrange ADM and smoothing technique to solve this problem. As the research deeper, non-square norm minimization was emerged, and some scholars extended the interior-point method and ADM onto this problem.In this thesis,we try to extend the smoothing technique onto the problem of mini-mizing the non-square matrix2-norm. First, construct the smooth approximation func-tion of non-smooth problem; and then, we give the gradient and Hessian matrix of smooth function, using the symmetrical technique and character of spectral function; last, we combine the inexact Newton method to present some numerical experiments, and show that this method is practicable.