A New Class of Scaling Matrices for Scaled Trust Region Algorithms

TL;DR

This paper introduces a new affine scaling matrix for interior point methods, combining properties of existing matrices to improve performance in solving nonlinear systems with bounds, supported by numerical experiments.

Contribution

The paper proposes a novel convex combination of known scaling matrices, enhancing their properties for better algorithmic performance.

Findings

New scaling matrix outperforms existing matrices in test problems

Inherited properties improve convergence and stability

Numerical results demonstrate superior efficiency

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 additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.