Mini-workshop: Applied Koopmanism. Abstracts from the mini-workshop held February 7--13, 2016
type: Item
instance of: scholarly article
title: Mini-workshop: Applied Koopmanism. Abstracts from the mini-workshop held February 7--13, 2016
zbMATH Open document ID: 1380.00065
DOI: 10.4171/OWR/2016/7
published in: Oberwolfach Reports
publication date: 2018-02-21T00:00:00Z
review text: Summary: Koopman and Perron-Frobenius operators are linear operators that encapsulate dynamics of nonlinear dynamical systems \textit{without loss of information}. This is accomplished by embedding the dynamics into a larger infinite-dimensional space where the focus of study is shifted from trajectory curves to measurement functions evaluated along trajectories and densities of trajectories evolving in time. Operator-theoretic approach to dynamics shares many features with an optimization technique: the Lasserre moment-sums-of-squares (SOS) hierarchies, which was developed for numerically solving non-convex optimization problems with semialgebraic data. This technique embeds the optimization problem into a larger primal semidefinite programming (SDP) problem consisting of measure optimization over the set of globally optimal solutions, where measures are manipulated through their truncated moment sequences. The dual SDP problem uses SOS representations to certify bounds on the global optimum. This workshop highlighted the common threads between the operator-theoretic dynamical systems and moment-SOS hierarchies in optimization and explored the future directions where the synergy of the two techniques could yield results in fluid dynamics, control theory, optimization, and spectral theory.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 37M25
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 37-06
Mathematics Subject Classification ID: 14P10
zbMATH DE Number: 6841672
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/owr/2016/7
OpenAlex ID: W2530279526
description: scientific article; zbMATH DE number 6841672