A damped semismooth Newton method for the Brugnano–Casulli piecewise linear system

Abstract

The piecewise linear system is a nonsmooth but semismooth equation. In this paper, a damped semismooth Newton method is presented for solving a class of piecewise linear systems. Under appropriate conditions, both monotone convergence and finite termination properties are investigated for the proposed method.

A generalized Newton method for a class of discrete-time linear complementarity systems

“…Generalized Newton methods have been extensively studied for solving piecewise linear systems, such as linear complementarity problems arising from the discretization of American options pricing problems [23] and obstacle problems [16], the discrete HJB equation [2,29] and piecewise linear systems arising in the numerical solution of the free-surface hydrodynamics models [3,4,28]. It has been verified that this type of methods possess a finite termination property, i.e., they are able to find a solution in a finite number of iterations under suitable conditions [2,3,10,12,27,28]. In addition, if the generalized Jacobi matrix is an M-matrix, these methods converge globally.…”