Finite termination and global monotonicity of Newton-type methods for solving hybrid piecewise linear systems

Abstract

In the present paper, we give a detailed theoretical analysis for some Newton-type procedures for certain piecewise linear systems. Under rather general assumptions, the iterates are well defined and monotonically converge to the exact solution of the given systems. This procedure is shown to have a finite termination property, i.e. it converges to the exact solution in a finite number of steps.

Keywords:

• M-matrix
• hybrid piecewise linear systems
• Newton-type methods
• finite termination
• global monotonicity

2000 AMS Subject Classifications :

• 90C33
• 90C53
• 90C06