An Affine Scaling Interior Method for Solving System of Bound-Constrained Semismooth Equations

In this paper, we present an affine scaling interior algorithm for solving bound-constrained semi-smooth equations. In this algorithm, we develop Inexact Newton Method that is combined with a line search technique. The affine technique and step back-tracking along inexact Newton steps are used. If iteration direction doesn´t satisfy rules expected, the method allows switch to new step in which both line search and interior point backtracking techniques decrease function values. The paper presents a full proof of the method with both global and local super-linear convergences.