Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques
Optimization and Control
2025-01-09 v1
Abstract
We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author under the supervision of Ya-xiang Yuan. At each iteration, the framework defines a (low-dimensional) subspace based on an approximate gradient, and then solves a subproblem in this subspace to generate a new iterate. We sketch the global convergence and worst-case complexity analysis of the framework, elaborate on its implementation, and present some numerical results on solving problems with dimensions as high as 10^4 using only inaccurate function values.
Cite
@article{arxiv.2501.04536,
title = {Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques},
author = {Zaikun Zhang},
journal= {arXiv preprint arXiv:2501.04536},
year = {2025}
}