English

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}
}
R2 v1 2026-06-28T08:44:33.545Z