A New Class of Scaling Matrices for Scaled Trust Region Algorithms

Abstract

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies all the desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.