In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained optimization problem, global exponential convergence in expectation and global exponential practical convergence of the variance of the trajectories are proven. The theoretical results are complemented by numerical simulations for one- and multi-dimensional quadratic and non-quadratic objective functions.
@article{arxiv.2410.20572,
title = {Time-delay Induced Stochastic Optimization and Extremum Seeking},
author = {Naum Dimitrieski and Michael Reyer and Mohamed-Ali Belabbas and Christian Ebenbauer},
journal= {arXiv preprint arXiv:2410.20572},
year = {2024}
}
Comments
Preprint to be submitted to the 2025 European Control Conference (ECC25)