Efficient Parameter Selection for Scaled Trust-Region Newton Algorithm in Solving Bound-constrained Nonlinear Systems

TL;DR

This paper studies how to choose parameters for the scaled trust-region Newton algorithm to efficiently solve bound-constrained nonlinear equations, analyzing performance across many test problems.

Contribution

It provides an empirical analysis of parameter effects on STRN performance and recommends the most effective parameter choice.

Findings

No universally best parameter value exists.

Parameter effectiveness varies across different problems.

Recommended parameter values improve algorithm efficiency.

Abstract

We investigate the problem of parameter selection for the scaled trust-region Newton (STRN) algorithm in solving bound-constrained nonlinear equations. Numerical experiments were performed on a large number of test problems to find the best value range of parameters that give the least algorithm iterations and function evaluations. Our experiments demonstrate that, in general, there is no best parameter to be chosen and each specific value shows an efficient performance on some problems and weak performance on other ones. In this research, we report the performance of STRN for various choices of parameters and then suggest the most effective one.