On complexity constants of linear and quadratic models for derivative-free trust-region algorithms
Abstract
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing complexity results hide the dimensions of the problem. This work organizes several results in literature about bounds that appear in derivative-free trust-region algorithms based on linear and quadratic models. All the constants are given explicitly by the quality of the sample set, dimension of the problem and number of sample points. We extend some results to allow "inexact" interpolation sets. We also provide a clearer proof than those already existing in literature for the underdetermined case.
Keywords
Cite
@article{arxiv.2205.11358,
title = {On complexity constants of linear and quadratic models for derivative-free trust-region algorithms},
author = {A. E. Schwertner and F. N. C. Sobral},
journal= {arXiv preprint arXiv:2205.11358},
year = {2024}
}
Comments
The preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Optimization Letters, and is available online at https://doi.org/10.1007/s11590-024-02147-4