Implementace semihladké Newtonovy metody

Abstract

The goal of this work is an implementation of semismooth Newton method. Newton method is a numerical method, which is proposed to solve the system of equations. This method is not able to solve the system of equations with nodifferentable functions. Because of it we will define semismooth Newton metod which is based on Clarke calculus. I need some basic definitions from Clarke calculus like generalized derivative, generalized gradient and generalized Jacobian. Then I describe "classical" Newton method and mainly semismooth Newton method. The next part of my work is devoted to implementation of semismooth Newthon method in program Matlab and comparison of solutions based on generalized Jacobian and numerical approximation of generalized Jacobian. In the end of my work I show you some numerical experiments with deformation of string in contact with rigid obstacle.