An approximate Newton method for solving non-smooth equations with infinite max functions

Abstract

In this paper, a new version of an approximate Newton method for solving non-smooth equations with infinite max function is presented. This method uses a difference approximation of the generalized Jacobian based on a weak consistently approximated Jacobian. Numerical example is reported for the generalized Newton method using two versions of approximation.

Keywords:

• non-smooth equation
• semismooth function
• weak consistently approximated Jacobian
• difference approximation
• superlinear convergence

2000 AMS Subject Classifications :

• 65H10
• 90C33

ACM Computing Classification System Codes :

• G.1.5
• G.1.2
• F.2.1