Gradient Approximation and Multi-Variable Derivative-Free Optimization based on Non-Commutative Maps
Abstract
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps is introduced. The procedure is based on the construction of an exploration sequence to specify where the objective function is evaluated and the definition of so-called gradient generating functions which are composed with the objective function such that the procedure mimics a gradient descent algorithm. Various theoretical properties of the proposed class of algorithms are investigated and numerical examples are presented.
Cite
@article{arxiv.2006.00801,
title = {Gradient Approximation and Multi-Variable Derivative-Free Optimization based on Non-Commutative Maps},
author = {Jan Feiling and Mohamed-Ali Belabbas and Christian Ebenbauer},
journal= {arXiv preprint arXiv:2006.00801},
year = {2021}
}
Comments
25 pages; Matlab Toolbox attached. To view attachments, please download the files listed under "Ancillary Files"