## Paul Manns

Assistant Professor (Juniorprofessor) at the
Chair of Numerical Analysis and Optimization

Faculty of Mathematics

TU Dortmund University

Address: Vogelpothsweg 87, 44227 Dortmund

Phone: +49 231 755 7242

Email: paul.manns **at symbol** tu-dortmund.de

## Bio

Paul did his Bachelor studies in Computer Science (diploma 2013) and Master studies in Computational Engineering (diploma 2015) at Technical University of Darmstadt. Afterwards, he was a research associate at the research group Optimization in Robotics and Biomechanics at Heidelberg University for a year (2016-2017). In April 2017, he joined the Institute for Mathematical Optimization at Technical University of Braunschweig as a research associate, where he finished his PhD in 2019. From August 2019 to November 2019, he was on a research stay at Argonne National Laboratory. In September 2020, Paul left Technical University of Braunschweig and joined the Mathematics and Computer Science Division of Argonne National Laboratory as James H Wilkinson Fellow in Scientific Computing. In September 2021, Paul assumed the position as assistant professor at TU Dortmund University.

## Research Areas

- Mixed-integer PDE-constrained optimization problems
- Trust-region algorithms
- Regularization techniques

## Publications

### Preprints / under review / in revision

- P. Manns, V. Nikolić. Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control. (view online)
- F. Bestehorn, C. Hansknecht, C. Kirches, P. Manns. Non-uniform grid refinement for the combinatorial integral approximation. (view online)
- S. Hillbrecht, P. Manns, C. Meyer. Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis. (view online)
- L. Bociu, P. Manns, M. Severitt, S. Strikwerda. Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems. (view online)

### Refereed Journals

- C. Hansknecht, C. Kirches, P. Manns. Convergence of successive linear programming algorithms for noisy functions. Computational Optimization and Applications, 2024. (accepted) (preprint) (view online)
- P. Manns, A. Schiemann (née Müller). On integer optimal control with total variation regularization on multi-dimensional domains. SIAM Journal on Control and Optimization, 61 (6), pp. 3415–3441, 2023. (preprint) (view online)
- P. Manns, M. Hahn, C. Kirches, S. Leyffer, S. Sager. On convergence of binary trust-region steepest descent. Journal of Nonsmooth Analysis and Optimization, 4 (2), 2023. (view online)
- P. Manns, T. Surowiec. On binary optimal control in Hs(0,T), s < 1/2. Comptes Rendus Mathématique, 361.G9, pp. 1531-1540, 2023. (preprint)
- M. Severitt, P. Manns. Efficient solution of discrete subproblems arising in integer optimal control with total variation regularization. INFORMS Journal on Computing, 35 (4), 2023. (view online) (preprint)
- S. Leyffer, and P. Manns. Sequential Linear Integer Programming for Integer Optimal Control with Total Variation Regularization. ESAIM: Control, Optimisation, and Calculus of Variation, 28 (66), 2022. (view online) (preprint)
- P. Manns, and S. Ulbrich. A simplified Newton method to generate snapshots for POD models of semilinear optimal control problems. SIAM Journal on Numerical Analysis, 60 (5), pp. 2807–2833, 2022. (view online) (preprint)
- C. Kirches, J. Larson, S. Leyffer, and P. Manns. Sequential linearization method for bound-constrained mathematical programs with complementarity constraints. SIAM Journal on Optimization 32 (1), pp. 75–99, 2022. (view online) (preprint) (version with appendices)
- P. Manns. Relaxed multibang regularization for the combinatorial integral approximation. SIAM Journal on Control and Optimization, 59 (4), pp. 2645–2668, 2021. (preprint) (view online)
- F. Bestehorn, C. Hansknecht, C. Kirches, and P. Manns. Switching cost aware rounding for relaxations of mixed-integer optimal control problems: the two-dimensional case. IEEE Control Systems Letters, 6, pp. 548–553, 2021. (preprint) (view online)
- S. Leyffer, P. Manns, and M. Winckler. Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation. Computational Optimization and Applications, 79, pp. 193–221, 2021. (view online)
- C. Kirches, P. Manns, and S. Ulbrich. Compactness and convergence rates in the combinatorial integral approximation decomposition. Mathematical Programming, 188, pp. 569–598, 2021. (preprint) (view online)
- F. Bestehorn, C. Hansknecht, C. Kirches, and P. Manns. Mixed-integer optimal control problems with switching costs: A shortest path approach. Mathematical Programming, 188, pp. 621–652, 2021. (preprint) (view online)
- P. Manns, C. Kirches, and F. Lenders. Approximation properties of sum-up rounding in the presence of vanishing constraints. Mathematics of Computation, 90, pp. 1263–1296, 2021. (preprint) (view online)
- D. Lorenz, P. Manns, and C. Meyer. Quadratically regularized optimal transport. Applied Mathematics & Optimization, 83, pp. 1919–1949, 2021. (preprint) (view online)
- P. Manns, and C. Kirches. Multidimensional sum-up rounding for elliptic control systems. SIAM Journal on Numerical Analysis, 58(6), pp. 3427–3447, 2020. (preprint) (view online)
- C. Kirches, F. Lenders, and P. Manns. Approximation properties and tight bounds for constrained mixed-integer optimal control. SIAM Journal on Control and Optimization, 58(3), pp. 1371–1402, 2020. (view online)
- P. Manns, and C. Kirches. Improved regularity assumptions for partial outer convexification of mixed-integer PDE-constrained optimization problems. ESAIM: Control, Optimisation and Calculus of Variations, 26 (32), 2020. (view online)
- M. Kudruss, P. Manns, and C. Kirches. Efficient derivative evaluation for rigid-body dynamics based on recursive algorithms subject to kinematic and loop constraints. IEEE Control Systems Letters, 3 (3), pp. 619–624, 2019. (view online)
- P. Manns, M. Sreenivasa, M. Millard, and K. Mombaur. Motion optimization and parameter identification for a human and lower-back exoskeleton model. IEEE Robotics and Automation Letters, 2 (3), pp. 1564–1570, 2017. (preprint) (view online)

### Refereed Book Chapters

- M. Hahn, C. Kirches, P. Manns, S. Sager, and C. Zeile. Decomposition and approximation for PDE-constrained mixed-integer optimal control. M. Hintermüller et al. (eds.) Non-Smooth and Complementarity-Based Distributed Parameter Systems. Volume 172 of International Series of Numerical Mathematics, pp. 283–305, 2022. (view online)

### Refereed Proceedings

- P. Manns. Asymptotics of rounding algorithms for integer control problems in the presence of convexified pointwise mixed constraints. Proceedings in Applied Mathematics and Mechanics, 2020. (view online)
- F. Bestehorn, C. Hansknecht, C. Kirches, and P. Manns. A switching cost aware rounding method for relaxations of mixed-integer optimal control problems. Proceedings of the 58th IEEE Conference on Decision and Control (CDC 2019), pp. 7134-7139, 12, 2019. (view online)
- P. Manns, and C. Kirches. Multi-dimensional sum-up rounding using Hilbert curve iterates. Proceedings in Applied Mathematics and Mechanics, 2019. (view online)
- P. Manns, and K. Mombaur. Towards discrete mechanics and optimal control for complex models. Proceedings of the 20th IFAC World Congress. IFAC-PapersOnLine, 50 (1), pp. 4812 - 4818, 2017. (view online)
- M. Sreenivasa, M. Millard, P. Manns, and K. Mombaur. Optimizing wearable assistive devices with neuromuscular models and optimal control. Converging Clinical and Engineering Research on Neurorehabilitation II, pp. 627–632, Springer, 2017. (view online)
- P. Manns, and K. Hamacher. Evolving smoothing kernels for global optimization. European Conference on the Applications of Evolutionary Computation, pp. 56–72, 2016. (view online)
- S. Kohlbrecher, F. Kunz, D. Koert, C. Rose, P. Manns, K. Daun, J. Schubert, A. Stumpf, and O. von Stryk. Towards highly reliable autonomy for urban search and rescue robots. Robot Soccer World Cup, pp. 118–129, 2014. (view online)
- L. Patzina, S. Patzina, T. Piper, and P. Manns. Model-based generation of run-time monitors for AUTOSAR. European Conference on Modelling Foundations and Applications, pp. 70–85, 2013. (view online)
- T. Piper, S. Winter, P. Manns, and N. Suri. Instrumenting AUTOSAR for dependability assessment: A guidance framework. IEEE/IFIP International Conference on Dependable Systems and Networks (DSN 2012), pp. 1–12, 2012. (view online)

### Other

- P. Manns, F. Bestehorn, C. Hansknecht, C. Kirches, and F. Lenders. Approximation properties of sum-up rounding and consequences for mixed-integer PDE-constrained optimization. In: L. Liberti and S. Sager and A. Wiegele (eds.), Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics, Oberwolfach Reports, 26 pp. 40–42, 2019. (view online)
- P. Manns. Approximation Properties of Sum-Up Rounding. 2019. Dissertation, Technische Universität Carolo-Wilhelmina zu Braunschweig (view online)
- S. Kohlbrecher, C. Rose, D. Koert, P. Manns, F. Kunz, B. Wartusch, K. Daun, A. Stumpf, and O. von Stryk. RoboCup Rescue 2016 Team Description Paper Hector Darmstadt. 2016.
- P. Manns. A Newton's method in snapshot generation for reduced order models in control of Navier-Stokes equations. Master's Thesis. Technische Universität Darmstadt. 2015.
- P. Manns. Evolutionary algorithms to optimize the Diffusion-Equation-Method. Bachelor's Thesis. Technische Universität Darmstadt. 2013.

## Talks

09/2023 | Simplified Newton Method for POD Computation in (Integer) Optimal Control. 6th European Conference on Computational Optimization (EUCCO), Heidelberg. |

07/2023 | A Trust-region Framework for Perimeter Regularization of Distributed Integer-valued Parameters in Topology Optimization: Analysis, Numerics, and Limits. 17th U.S. National Congress on Computational Mechanics (17USNCCM), Albuquerque, NM. |

03/2023 | Trust-Region Method for PDE-Constrained Optimization with Total Variation Regularization of Distributed Integer-Valued Parameters. SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam. |

07/2022 | Γ-Convergence in Regularized Bilevel Optimal Transport. ICCOPT 2022, Bethlehem, PA. |

07/2022 | Improved Regularity for Sequential Linear Integer Programming for Integer Optimal Control. IFIP TC 7 2022, Warsaw. |

07/2021 | Total Variation Regularization for Integer Control Problems with One-Dimensional Domains. SIAM Annual Meeting 2021, virtual. |

03/2021 | Regularization for Integer Optimal Control. GAMM Annual Meeting 2020/2021, virtual. |

03/2021 | Regularization for the Combinatorial Integral Approximation. SIAM Conference on Computational Science and Engineering (CSE21), virtual. |

12/2019 | Weak Approximation Techniques for Mixed-Integer PDE-Constrained Optimization. SIAM Conference on Analysis of Partial Differential Equations (PD19), La Quinta, CA. |

11/2019 | Approximation Techniques for Mixed-Integer PDE-Constrained Optimization. Laboratory for Applied Mathematics, Numerical Software, and Statistics, Argonne National Laboratory, IL. |

08/2019 | A continuous perspective on Mixed-Integer Optimal Control. International Conference On Continuous Optimization – ICCOPT 2019, Berlin. |

02/2019 | Multi-dimensional Sum-Up Rounding. GAMM Annual Meeting 2019, Vienna. |

10/2018 | Non-smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes. DFG SPP 1962 Annual Meeting 2018, Beetz-Sommerfeld. |

09/2018 | A Linear Bound on the Integrality Gap for Sum-Up Rounding. European Conference on Computational Optimization – EUCCO 2018, Trier. |

07/2018 | Regularity Assumptions for Partial Outer Convexification of semilinear-constrained MIOCPs. IFIP TC 7 Conference 2018 on System Modelling and Optimization, Essen. |

06/2018 | Improved Regularity Assumptions for Partial Outer Convexification of MIPDECOs. International Symposium on Mathematical Programming – ISMP 2018, Bordeaux. |

10/2017 | Non-smooth Methods for Complementarity Formulations of Switched-Advection-Diffusion Processes. DFG SPP 1962 Annual Meeting 2018, Beetz-Sommerfeld. |

07/2017 | Towards Discrete Mechanics and Optimal Control for Complex Problems. 20th IFAC World Congress, Toulouse |

### Invited Talks

04/2023 | Recent Advances in Mixed-integer PDE-constrained Optimization: Regularization, Stationarity, and Algorithms. Center for Mathematics and Artificial Intelligence. George Mason University. |

03/2023 | Regularization for distributed parameter identification problems with integralities. Optimal Control Group. BTU Cottbus. |

03/2023 | Regularization in Integer Optimal Control – Lessons Learned and Challenges Ahead. Optimization in Oslo Seminar. Simula Research Laboratory. |

12/2022 | Regularization for Distributed Parameter Identification Problems with Integralities. Faculty of Mathematics. Chemnitz University of Technology. |

11/2022 | Mixed-integer PDE-constrained Optimization with Total Variation Regularization: Stationarity and Trust-region Algorithms. Optimal Control of Partial Differential Equations Group. University of Duisburg-Essen. |

08/2022 | On Total Variation Regularization for PDE-constrained optimization with Integer Controls. NCSU Differential Equations/Nonlinear Analysis Seminar. North Carolina State University. |

03/2022 | Sequential Integer Linear Programming with Accelerations by Shortest Path Computations for Integer Optimal Control on One-dimensional Domains. Systems Control and Optimization Laboratory. University of Freiburg. |

12/2021 | Sequential Linear Integer Programming for Integer Optimal Control – the 1D Case. HU Berlin. |

11/2021 | Simplified Newton Method for POD Computation in Optimal Control. Mathematics and Computer Science Division, Argonne National Laboratory, IL. |

08/2021 | A Trust-region Method with Subproblems that are Integer Linear Programs for TV-regularized Integer Optimal Control. Technical University of Braunschweig. |

06/2021 | Recent Progress and Perspectives on Regularization for Mixed-integer PDE-constrained Optimization. Clausthal University of Technology. |

05/2020 | Perspectives for Approximation of Integer Optimal Control Problems. University of Göttingen. |

01/2020 | Promising Frontiers in Approximation Techniques for Mixed-Integer Optimal Control. Mathematics and Computer Science Division, Argonne National Laboratory, IL. |

11/2019 | Approximation Techniques for Mixed-Integer PDE-Constrained Optimization. Center for Computing Research, Sandia National Laboratories, NM. |

06/2019 | Approximation Properties of Sum-Up Rounding and Consequences for Mixed-Integer PDE-Constrained Optimization. Workshop 26/2019, Mixed-integer Non-linear Optimization: A Hatchery for Modern Mathematics, Mathematisches Forschungszentrum Oberwolfach. |

12/2018 | Approximation Properties of Sum-Up Rounding. Oberseminar Optimierung, Technische Universität Dortmund. |

## Teaching

Term | Course | Role | Institution |
---|---|---|---|

Winter 2023/2024 | Nonlinear Optimization | Lecturer | TU Dortmund |

Summer 2023 | Convex Analysis | Lecturer | TU Dortmund |

Winter 2022/2023 | Practical Optimization | Lecturer | TU Dortmund |

Winter 2022/2023 | Geometric Optimization | Lecturer | TU Dortmund |

Summer 2022 | Optimization | Lecturer | TU Dortmund |

Winter 2021/2022 | Nonlinear Optimization | Lecturer | TU Dortmund |

Summer 2020 | Introduction to Optimal Transport and Gradient Flows | Lecturer | TU Braunschweig |

Summer 2019 | Introduction to Nonlinear Optimization | Teaching Assistant | TU Braunschweig |

Summer 2018 | Introduction to Nonlinear Optimization | Teaching Assistant | TU Braunschweig |

Winter 2017/2019 | Dynamic Optimization | Teaching Assistant | TU Braunschweig |

Summer 2018 | Computer-Oriented Mathematics | Teaching Assistant | TU Braunschweig |