An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods
Optimization and Control
2024-10-10 v6
Abstract
This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, including NEWUOA, BOBYQA, LINCOA, and COBYQA. Our analysis provides a theoretical justification for this choice.
Keywords
Cite
@article{arxiv.2302.09992,
title = {An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods},
author = {Tom M. Ragonneau and Zaikun Zhang},
journal= {arXiv preprint arXiv:2302.09992},
year = {2024}
}