Optimization based on Non-Commutative Maps
143 pages, year of publication: 2021
price: 48.50 €
Powerful optimization algorithms are key ingredients in science and engineering applications. In this thesis, we develop a novel class of discrete-time, derivative-free optimization algorithms relying on gradient approximations based on non-commutative maps–inspired by Lie bracket approximation ideas in control systems. Those maps are defined by function evaluations and applied in such a way that gradient descent steps are approximated, and semi-global convergence guarantees can be given. We supplement our theoretical findings with numerical results. Therein, we provide several algorithm parameter studies and tuning rules, as well as the results of applying our algorithm to challenging benchmarking problems.
Jan Feiling received the Bachelor (B.Sc.) and Master (M.Sc.) degree in Engineering Cybernetics from University of Stuttgart in 2014 and 2017, respectively. During this time, he has served as a visiting scholar at National University of Singapore (2014) and University of California (2016–2017). From May 2017 until April 2020 he was part of the Institute for Systems Theory and Automatic Control, University of Stuttgart as a Ph.D. candidate and employed at the R&D department of the Porsche AG. In November 2019 he joined as a full time professional venture architect the company builder of Porsche Digital GmbH, Forward31 in Berlin. His research interests lie in the area of optimization, control theory, and machine learning.