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.