Set-Valued Numerical Analysis
start of the project: 2008
funding institution:
until 2017: The Hermann Minkowski Center for Geometry in Tel Aviv, Israel;
DAAD; Bulgarian Academy of Sciences
PROJECT MEMBERS
principal investigator
project members
Dr. Elza Farkhi (School of Mathematical Sciences, Tel Aviv University, Israel)Dr. Alona Mokhov (Afeka Academic College of Engineering, Tel Aviv, Israel)
Dr. Gilbert Perria (project member until 09/2010 )
AIMS OF THE PROJECT
The project leader continues the project which was started 1995 by Prof. Dr. Frank Lempio.
Modelling of differential equations with discontinuous right-hand sides, dynamical systems with uncertainties, non-smooth optimization problems, and optimal control problems lead to differential equations with set-valued right-hand sides, so-called differential inclusions.
Within the research project "Set-Valued Numerical Analysis", differential inclusions are investigated qualitatively and quantitatively, and algorithms for their numerical solution are developed.
The numerical solution of such differential inclusions requires algorithms from set-valued numerical analysis, especially integration techniques for set-valued integrands and interpolation techniques for set-valued maps, based e.g. on set-valued finite element methods, set-valued divided differences and embeddings of convex compact sets. Especially, one focus is laid on the approximation of reachable sets at a given time which consist of all endpoints of admissible trajectories of a differential inclusion.
There are strong connections to the direcet discretization of optimal control problems, e.g. in questions on the (order of) convergence of the optimal control/trajectory of the discrete problems to the corresponding optimal control/trajectory of the continuous problem.
MINISYMPOSIA/SESSIONS
The project members organized the following minisymposia and sessions on set-valued numerics.
- invited Special
Session “Set-valued mappings in approximation, control and optimization“
conference: 16th Viennese Conference on Optimal Control and Dynamic Games (VC 2026) in Wien, Austria
chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)
- invited Special
Session “Set-valued mappings in control and optimization“
conference: 15th Viennese Conference on Optimal Control and Dynamic Games (VC 2026) in Wien, Austria
chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)
- invited Special
Session "Approximation of Differential Inclusions and Control Problems 1-2"
conference: 14th Viennese Conference on Optimal Control and Dynamic Games (OCDGND 2018) in Wien, Austria
chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)
- invited Special Session
"Set-Valued Numerics and Control 1-2"
conference: 13th Viennese Workshop on Optimal Control, and Dynamic Games (OCDGND 2015) in Wien, Austria
chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)
- invited
Minisymposium "Set-dynamic Approaches with Applications in Car Engineering"
conference: XXXIV Dynamics Days Europe (2014) in Bayreuth
chair: Robert Baier, Thomas Lorenz (RheinMain Unversity in Wiesbaden)
- invited Special
Session "Set-Valued Analysis for Optimal Control 1-2"
conference: 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics (OCDGND 2012) in Wien, Austria
chair: Robert Baier
- invited Special Session
MB-39 "Set-Valued Analysis for Control Problems"
conference: 24th European Conference on Operational Research (EURO XXIV, 2010) in Lisbon, Portugal
chair: Robert Baier
- Workshop
"Set-valued Numerical Analysis and Robust Optimal Control"
realization within the HIM Junior Trimester Program "Computational Mathematics" (2008) in Bonn, Germany
organization: Robert Baier, Thomas Lorenz (formerly: University of Heidelberg)
LINKS
- The Hermann Minkowski Center
of Geometry (Minerva Center at the Tel Aviv University)
- Minerva
Foundation
- Hausdorff Research Institute for Mathematics (HIM) in Bonn, Germany