S. Peitz,   Exploiting structure in multiobjective optimization and optimal control. 2017.

L. Biasco and L. Di Gregorio, “A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation,” Archive for Rational Mechanics and Analysis, pp. 303–362, 2009.

J. Eckstein et al., “A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles,”10.1016/j.protcy.2016.08.059__in Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 2016, vol. 26, pp. 465–472, doi:10.1016/j.protcy.2016.08.059 .

M. Dellnitz, G. Froyland, and S. Sertl, “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator,” in Equadiff 99, 2000.

B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in Numerical and Evolutionary Optimization – NEO 2017, 2018.

K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376. 2024.

O. Schütze, E. Talbi, G. T. Pulido, C. C. Coello, and L. V. Santana-Quintero, “A Memetic PSO Algorithm for Scalar Optimization Problems,” in 2007 IEEE Swarm Intelligence Symposium, 2007.

M. Dellnitz, S. Ober-Blöbaum, M. Post, O. Schütze, and B. Thiere, “A multi-objective approach to the design of low thrust space trajectories using optimal control,” Celestial Mechanics and Dynamical Astronomy, pp. 33–59, 2009.

S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A multiobjective MPC approach for autonomously driven electric vehicles,”10.1016/j.ifacol.2017.08.1526__Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), vol. 50, no. 1, pp. 8674–8679, 2017, doi:10.1016/j.ifacol.2017.08.1526 .

S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).,” IFAC-PapersOnLine, pp. 8674–8679, 2017.

S. Ober-Blöbaum and A. Seifried, “A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties,” in 2013 European Control Conference (ECC), 2013.

K. Witting, B. Schulz, M. Dellnitz, J. Böcker, and N. Fröhleke, “A new approach for online multiobjective optimization of mechatronic systems,” International Journal on Software Tools for Technology Transfer, pp. 223–231, 2008.

O. Schütze, “A New Data Structure for the Nondominance Problem in Multi-objective Optimization,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.

B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,”10.1007/s10589-024-00552-0__Computational Optimization and Applications, 2024, doi:10.1007/s10589-024-00552-0 .

M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric periodic points,” Nonlinearity, pp. 1067–1075, 1995.

S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled  oscillator networks,” arXiv:2306.03320. .

S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” SIAM Journal on Applied Dynamical Systems, pp. 117–160, 2004.

O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,” ESAIM: Control, Optimisation and Calculus of Variations, pp. 259–270, 2004.

L. Grüne and O. Junge, “A set oriented approach to optimal feedback stabilization,” Systems &; Control Letters, pp. 169–180, 2005.

M. Dellnitz, S. Klus, and A. Ziessler, “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty,” SIAM Journal on Applied Dynamical Systems, pp. 120–138, 2017.

R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,”10.1137/19m1247139__SIAM Journal on Applied Dynamical Systems, pp. 705–723, 2020, doi:10.1137/19m1247139 .

M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of unstable manifolds and global attractors,” Numerische Mathematik, vol. 75, pp. 293–317, 1997.

B. Krauskopf et al., “A Survey of Methods for Computing (un)stable Manifolds of Vector Fields,” International Journal of Bifurcation and Chaos, pp. 763–791, 2005.

S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction,” Mathematical and Computational Applications, vol. 23, no. 2, 2018.

K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “A variational approach to define robustness for parametric multiobjective optimization problems,” Journal of Global Optimization, pp. 331–345, 2013.

F. Noé and F. Nüske, “A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems,” Multiscale Modeling &; Simulation, pp. 635–655, 2013.

M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,” Nonlinearity, pp. 1039–1066, 1995.

S. Vieluf et al., “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control,” Neuroscience, pp. 203–213, 2018.

M. Dellnitz and O. Junge, “Almost Invariant Sets in Chua’s Circuit,” International Journal of Bifurcation and Chaos, pp. 2475–2485, 1997.

R. Guder, M. Dellnitz, and E. Kreuzer, “An adaptive method for the approximation of the generalized cell mapping,” Chaos, Solitons &; Fractals, pp. 525–534, 1997.

M. Dellnitz and O. Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures,” Computing and Visualization in Science, pp. 63–68, 1998.

O. Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence,” Dynamical Systems, pp. 213–222, 2001.

S. Klus, T. Sahai, C. Liu, and M. Dellnitz, “An efficient algorithm for the parallel solution of high-dimensional differential equations,” Journal of Computational and Applied Mathematics, pp. 3053–3062, 2011.

B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” Journal of Optimization Theory and Applications, vol. 188, pp. 696–723, 2021.

R. Timmermann and M. Dellnitz, “Analysis of team and player performance using recorded trajectory data,” in Performance Analysis of Sport IX, Part 8, Routledge, 2013.

S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions,” arXiv:1805.10118. 2018.

R. Preis, B. Monien, and S. Schamberger, “Approximation Algorithms for Multilevel Graph Partitioning,” in Handbook of Approximation Algorithms and Metaheuristics, 2007.

F. Demoures, F. Gay-Balmaz, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, and T. S. Ratiu, “Asynchronous variational Lie group integration for geometrically exact beam dynamics,” PAMM, pp. 45–46, 2013.

F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” The Journal of Chemical Physics, 2019.

M. Dellnitz, “Collisions of chaotic attractors,” Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg, pp. 411–428, 1994.

B. Gebken, Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization. 2022.

P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte, “Computation of Essential Molecular Dynamics by Subdivision Techniques,” in Computational Molecular Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.

M. Dellnitz and K. Witting, “Computation of robust Pareto points,” International Journal of Computing Science and Mathematics, 2009.

P. J. Aston and M. Dellnitz, “Computation of the dominant Lyapunov exponent via spatial integration using matrix norms,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, pp. 2933–2955, 2003.

M. Dellnitz, “Computational bifurcation of periodic solutions in systems with symmetry,” IMA Journal of Numerical Analysis, vol. 12, no. 3, pp. 429–455, 1992.

M. Dellnitz and B. Werner, “Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points,” Journal of Computational and Applied Mathematics, pp. 97–123, 1989.

T. Gail, S. Leyendecker, and S. Ober-Blöbaum, “Computing time investigations for variational multirate integration,” PAMM, pp. 43–44, 2013.

M. Dellnitz and R. Preis, “Congestion and Almost Invariant Sets in Dynamical Systems,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.

M. Dellnitz, K. Padberg, R. Preis, and B. Thiere, “Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem,” in Nonlinear Science and Complexity, Dordrecht, 2010.

T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for the traveling salesman problem,” Nonlinear Dynamics, 2019.

K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, and A. Trächtler, “Control strategies on stable manifolds for energy-efficient swing-ups of double pendula,” International Journal of Control, pp. 1886–1905, 2014.

S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data,” arXiv:1801.06419. 2018.

O. Schütze, M. Laumanns, C. A. Coello Coello, M. Dellnitz, and E.-G. Talbi, “Convergence of stochastic search algorithms to finite size pareto set approximations,” Journal of Global Optimization, pp. 559–577, 2008.

O. Schütze, S. Mostaghim, M. Dellnitz, and J. Teich, “Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.

M. Dellnitz, O. Schÿfdtze, and T. Hestermeyer, “Covering Pareto Sets by Multilevel Subdivision Techniques,” Journal of Optimization Theory and Applications, pp. 113–136, 2005.

M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,” International Journal of Bifurcation and Chaos, pp. 1243–1247, 1995.

S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte, “Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.

S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control using Interpolated Koopman  Generators,” SIAM Journal on Applied Dynamical Systems, vol. 19, no. 3, pp. 2162–2193, 2020.

S. Klus et al., “Data-Driven Model Reduction and Transfer Operator Approximation,” Journal of Nonlinear Science, pp. 985–1010, 2018.

K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model predictive flow control with limited sensor data and online learning,” Theoretical and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.

M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models,” Mathematical and Computational Applications, vol. 26, no. 2, 2021.

R. Li et al., “Design and implementation of a hybrid energy supply system for railway vehicles,” in Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005.

O. Schütze, M. Vasile, O. Junge, M. Dellnitz, and D. Izzo, “Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach,” Engineering Optimization, pp. 155–181, 2009.

G. Froyland and M. Dellnitz, “Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles,” SIAM Journal on Scientific Computing, pp. 1839–1863, 2003.

B. Thiere, S. Ober-Blöbaum, and P. Pergola, “Detecting Initial Guesses for Trajectories in the (P)CRTBP,” in AIAA/AAS Astrodynamics Specialist Conference, 2010.

E. Barany, M. Dellnitz, and M. Golubitsky, “Detecting the symmetry of attractors,” Physica D: Nonlinear Phenomena, pp. 66–87, 1993.

G. Froyland, K. Padberg, M. H. England, and A. M. Treguier, “Detection of Coherent Oceanic Structures via Transfer Operators,” Physical Review Letters, 2007.

R. Elsässer, B. Monien, and R. Preis, “Diffusion Schemes for Load Balancing on Heterogeneous Networks,” Theory of Computing Systems, pp. 305–320, 2002.

A. Meyer, “Discontinuity Induced Bifurcations in Timed Continuous Petri Nets,” IFAC Proceedings Volumes, pp. 28–33, 2012.

S. Leyendecker, S. Ober-Blöbaum, J. E. Marsden, and M. Ortiz, “Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics,” in Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2007.

F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu, and Y. Weinand, “Discrete variational Lie group formulation of geometrically exact beam dynamics,” Numerische Mathematik, pp. 73–123, 2015.

A. Specht, S. Ober-Blobaum, O. Wallscheid, C. Romaus, and J. Bocker, “Discrete-time model of an IPMSM based on variational integrators,” in 2013 International Electric Machines &; Drives Conference, 2013.

K. Flasskamp, T. Murphey, and S. Ober-Blobaum, “Discretized switching time optimization problems,” in 2013 European Control Conference (ECC), 2013.

B. Klöpper, H. Podlogar, J. Gausemeier, and K. Witting, “Domain Spanning Search for the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing Systems,” in 2008 19th International Conference on Database and Expert Systems Applications, 2008.

M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement  learning,”10.1137/21M1412682__SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. 9–5, 2023, doi:10.1137/21M1412682 .

S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022.

M. Dellnitz and J. Scheurle, “Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom,” in Dynamics, Bifurcation and Symmetry, Dordrecht, 1994.

C. Goelz et al., “Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults,” Cognitive Neurodynamics, 2021.

K. Flaskamp and S. Ober-Blobaum, “Energy efficient control for mechanical systems based on inherent dynamical structures,” in 2012 American Control Conference (ACC), 2012.

T. Knoke, C. Romaus, J. Bocker, A. Dell’Aere, and K. Witting, “Energy Management for an Onboard Storage System Based on Multi-Objective Optimization,” in IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006.

T. Schneider, B. Schulz, C. Henke, K. Witting, D. Steenken, and J. Bocker, “Energy transfer via linear doubly-fed motor in different operating modes,” in 2009 IEEE International Electric Machines and Drives Conference, 2009.

C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,”10.1002/rnc.5197__International Journal of Robust and Nonlinear Control, vol. 30(17), pp. 7593–7618, 2020, doi:10.1002/rnc.5197 .

S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,”10.1002/rnc.5281__International Journal of Robust and Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi:10.1002/rnc.5281 .

M. Dellnitz, A. Hohmann, O. Junge, and M. Rumpf, “Exploring invariant sets and invariant measures,” Chaos: An Interdisciplinary Journal of Nonlinear Science, pp. 221–228, 1997.

G. Froyland, “Extracting Dynamical Behavior via Markov Models,” in Nonlinear Dynamics and Statistics, Boston, MA, 2001.

K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping,” arXiv:2307.00975. 2023.

K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,”10.1007/s10957-024-02389-3__Journal of Optimization Theory and Applications, 2024, doi:10.1007/s10957-024-02389-3 .

S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator,” in Lecture Notes in Control and Information Sciences, vol. 484, Cham: Springer, 2020, pp. 257–282.

M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” IMA Journal of Numerical Analysis, pp. 167–185, 2002.

S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification,” in 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019.

F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,”10.1007/s00332-022-09862-1__Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi:10.1007/s00332-022-09862-1 .

M. Dellnitz, I. Melbourne, and J. E. Marsden, “Generic bifurcation of Hamiltonian vector fields with symmetry,” Nonlinearity, pp. 979–996, 1992.

M. Dellnitz, J. E. Marsden, I. Melbourne, and J. Scheurle, “Generic Bifurcations of Pendula,” in Bifurcation and Symmetry, Basel, 1992.

M. Dellnitz and I. Melbourne, “Generic movement of eigenvalues for equivariant self-adjoint matrices,” Journal of Computational and Applied Mathematics, pp. 249–259, 1994.

L. Grüne and O. Junge, “Global Optimal Control of Perturbed Systems,” Journal of Optimization Theory and Applications, pp. 411–429, 2007.

I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, and T. Frauenheim, “Global optimization of silicon nanoclusters,” Applied Surface Science, pp. 108–113, 2004.

S. Sertl and M. Dellnitz, “Global Optimization using a Dynamical Systems Approach,” Journal of Global Optimization, pp. 569–587, 2006.

S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with Uncertainties,” in NEO 2016, 2017, pp. 159–182.

M. Dellnitz, M. H. Molo, P. Metzner, R. Preis, and C. Schütte, “Graph Algorithms for Dynamical Systems,” in Analysis, Modeling and Simulation of Multiscale Problems, 2006.

M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, and O. Schütze, “Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space,” Engineering Optimization, pp. 1117–1146, 2012.