Optimization by moving ridge functions: Derivative-free optimization for computationally intensive functions
Abstract
A novel derivative-free algorithm, optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to accelerate convergence of model-based optimization strategies. The dimension-reducing subspace is updated as the trust region moves through the function domain, allowing OMoRF to be applied to functions with no known global low-dimensional structure. Furthermore, its low computational requirement allows it to make rapid progress when optimizing high-dimensional functions. Its performance is examined on a set of test problems of moderate to high dimension and a high-dimensional design optimization problem. The results show that OMoRF compares favourably to other common derivative-free optimization methods, even for functions in which no underlying global low-dimensional structure is known.
Cite
@article{arxiv.2007.04893,
title = {Optimization by moving ridge functions: Derivative-free optimization for computationally intensive functions},
author = {James C. Gross and Geoffrey T. Parks},
journal= {arXiv preprint arXiv:2007.04893},
year = {2021}
}