TY - JOUR
AB - Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 8751
IS - 2
JF - Mathematical and Computational Applications
SN - 2297-8747
TI - A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction
VL - 23
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Kuklinski, Christiane
AU - Hochmuth, Reinhard
ED - Didaktik der Mathematik der Universität Paderborn, Fachgruppe
ID - 8574
T2 - Beiträge zum Mathematikunterricht 2018
TI - Auswirkungen von innovativen Vorlesungen für Lehramtsstudierende in der Studieneingangsphase
ER -
TY - CONF
AU - Schumacher, Jan
ID - 7766
T2 - Beiträge zum Mathematikunterricht 2018
TI - Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen
ER -
TY - JOUR
AU - Steffen, Eckhard
ID - 10142
IS - 1
JF - Australasian Journal of Combinatorics
TI - Approximating Vizing’s independence number conjecture
VL - 71
ER -
TY - CONF
AB - A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non‐smooth objective functionals. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results.
AU - Beermann, Dennis
AU - Dellnitz, Michael
AU - Peitz, Sebastian
AU - Volkwein, Stefan
ID - 8757
SN - 1617-7061
T2 - PAMM
TI - POD-based multiobjective optimal control of PDEs with non-smooth objectives
ER -
TY - CONF
AB - The transition from high school to university mathematics has proven to be difficult for many students but especially for pre-service secondary teachers. To support these students at mastering this transition, various universities have introduced support measures of various kinds. The WiGeMath project developed a taxonomy that makes it possible to describe and compare these measures concerning their goals as well as their frame characteristics. We will exemplify the use of the taxonomy in the description of one specific innovative measure that was part of the WiGeMath evaluations. Moreover, we will present first results concerning the goal-fulfilment of this measure concerning affective characteristics of the student cohort and their predominant beliefs.
AU - Kuklinski, Christiane
AU - Leis, Elena
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
AU - Biehler, Rolf
AU - Lankeit, Elisa
AU - Neuhaus, Silke
AU - Schaper, Niclas
AU - Schürmann, Mirko
ED - Durand-Guerrier, V.
ED - Hochmuth, R.
ED - Goodchild, S.
ED - Hogstad, N.M.
ID - 8575
KW - Beliefs.
KW - Motivational developments
KW - Novel approaches to teaching
KW - Teacher education
KW - Transition to and across university mathematics
T2 - Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018)
TI - Evaluating Innovative Measures in University Mathematics – The Case of Affective Outcomes in a Lecture focused on Problem-Solving
ER -
TY - JOUR
AB - There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.
AU - Fiol, M. A.
AU - Mazzuoccolo, Guiseppe
AU - Steffen, Eckhard
ID - 10129
IS - 4
JF - The Electronic Journal of Combinatorics
KW - Cubic graph
KW - Tait coloring
KW - Snark
KW - Boole coloring
KW - Berge's conjecture
KW - Tutte's 5-flow conjecture
TI - Measures of Edge-Uncolorability of Cubic Graphs
VL - 25
ER -
TY - GEN
AB - In a recent article, we presented a framework to control nonlinear partial
differential equations (PDEs) by means of Koopman operator based reduced models
and concepts from switched systems. The main idea was to transform a control
system into a set of autonomous systems for which the optimal switching
sequence has to be computed. These individual systems can be approximated very
efficiently by reduced order models obtained from data, and one can guarantee
equality of the full and the reduced objective function under certain
assumptions. In this article, we extend these results to continuous control
inputs using convex combinations of multiple Koopman operators corresponding to
constant controls, which results in a bilinear control system. Although
equality of the objectives can be carried over when the PDE depends linearly on
the control, we show that this approach is also valid in other scenarios using
several flow control examples of varying complexity.
AU - Peitz, Sebastian
ID - 16292
T2 - arXiv:1801.06419
TI - Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data
ER -
TY - BOOK
AU - Liebendörfer, Michael
ID - 8576
SN - 978-3-658-22506-3 978-3-658-22507-0
TI - Motivationsentwicklung im Mathematikstudium
ER -
TY - CHAP
AU - Biehler, Rolf
AU - Hochmuth, Reinhard
AU - Schaper, Niclas
AU - Kuklinski, Christiane
AU - Lankeit, Elisa
AU - Leis, Elena
AU - Liebendörfer, Michael
AU - Schürmann, Mirko
ED - Hanft, Anke
ED - Bischoff, Franziska
ED - Kretschmer, Stefanie
ID - 8569
T2 - 3. Auswertungsworkshop der Begleitforschung. Dokumentation der Projektbeiträge.
TI - Verbundprojekt WiGeMath: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase
ER -
TY - JOUR
AU - Frühbis-Krüger, Anne
AU - Liebendörfer, Michael
ID - 8571
IS - 63
JF - Computeralgebra-Rundbrief
TI - Minisymposium CAS in der Hochschullehre - ein Blick in die Praxis
ER -
TY - JOUR
AU - Jin, Ligang
AU - Mazzuoccolo, Giuseppe
AU - Steffen, Eckhard
ID - 10132
JF - Discussiones Mathematicae Graph Theory
SN - 1234-3099
TI - Cores, joins and the Fano-flow conjectures
VL - 38
ER -
TY - CHAP
AB - In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed in such a way that the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.
AU - Beermann, Dennis
AU - Dellnitz, Michael
AU - Peitz, Sebastian
AU - Volkwein, Stefan
ID - 8754
SN - 9783319753188
T2 - Reduced-Order Modeling (ROM) for Simulation and Optimization
TI - Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition
ER -
TY - GEN
AB - Kernel transfer operators, which can be regarded as approximations of
transfer operators such as the Perron-Frobenius or Koopman operator in
reproducing kernel Hilbert spaces, are defined in terms of covariance and
cross-covariance operators and have been shown to be closely related to the
conditional mean embedding framework developed by the machine learning
community. The goal of this paper is to show how the dominant eigenfunctions of
these operators in combination with gradient-based optimization techniques can
be used to detect long-lived coherent patterns in high-dimensional time-series
data. The results will be illustrated using video data and a fluid flow
example.
AU - Klus, Stefan
AU - Peitz, Sebastian
AU - Schuster, Ingmar
ID - 16293
T2 - arXiv:1805.10118
TI - Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions
ER -
TY - CHAP
AU - Frühbis-Krüger, Anne
AU - Kemper, Gregor
AU - Koepf, Wolfram
AU - Liebendörfer, Michael
ID - 8572
T2 - Beiträge zum Mathematikunterricht 2018
TI - CAS in der Hochschullehre - Ein Blick in die Praxis
ER -
TY - JOUR
AU - Jurgelucks, Benjamin
AU - Claes, Leander
AU - Walther, Andrea
AU - Henning, Bernd
ID - 6571
JF - Optimization Methods and Software
SN - 1055-6788
TI - Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation
ER -
TY - GEN
AU - Feldmann, Nadine
AU - Jurgelucks, Benjamin
AU - Claes, Leander
AU - Henning, Bernd
ID - 6595
T2 - Messtechnische Anwendungen von Ultraschall
TI - Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden
ER -
TY - JOUR
AB - Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.
AU - Klus, Stefan
AU - Gelß, Patrick
AU - Peitz, Sebastian
AU - Schütte, Christof
ID - 8755
IS - 7
JF - Nonlinearity
SN - 0951-7715
TI - Tensor-based dynamic mode decomposition
VL - 31
ER -
TY - GEN
AB - Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al.~have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and --
more importantly -- problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving.
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
ID - 16294
T2 - arXiv:1809.06238
TI - Explicit multiobjective model predictive control for nonlinear systems with symmetries
ER -
TY - CONF
AB - In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.
AU - Gebken, Bennet
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 8750
SN - 1860-949X
T2 - Numerical and Evolutionary Optimization – NEO 2017
TI - A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems
ER -
TY - CONF
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
ED - Göller, Robin
ED - Biehler, Rolf
ED - Hochmuth, Reinhard
ED - Rück, Hans-Georg
ID - 8559
T2 - Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings
TI - Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations
ER -
TY - CONF
AU - Jurgelucks, Benjamin
AU - Feldmann, Nadine
AU - Claes, Leander
AU - Henning, Bernd
AU - Walther, Andrea
ID - 6572
T2 - Proceedings of Meetings on Acoustics
TI - Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity
ER -
TY - JOUR
AB - We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption.
AU - Peitz, Sebastian
AU - Schäfer, Kai
AU - Ober-Blöbaum, Sina
AU - Eckstein, Julian
AU - Köhler, Ulrich
AU - Dellnitz, Michael
ID - 8756
IS - 1
JF - IFAC-PapersOnLine
SN - 2405-8963
TI - A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles
VL - 50
ER -
TY - CONF
AB - In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 8752
SN - 1860-949X
T2 - NEO 2016
TI - Gradient-Based Multiobjective Optimization with Uncertainties
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
AU - Biehler, Rolf
AU - Schaper, Niclas
AU - Kuklinski, Christiane
AU - Khellaf, Sarah
AU - Colberg, Christoph
AU - Schürmann, Mirko
AU - Rothe, Lukas
ED - Dooley, T.
ED - Gueudet, Ghislaine
ID - 8570
KW - Ziele der Lehre
T2 - Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1 – 5, 2017)
TI - A framework for goal dimensions of mathematics learning support in universities
ER -
TY - CONF
AU - Schumacher, Jan
ED - Kortenkamp, Ulrich
ED - Kuzle, Ana
ID - 7767
T2 - Beiträge zum Mathematikunterricht 2017
TI - Sinnkonstruktion beim Erkunden von Mustern und Strukturen
ER -
TY - JOUR
AU - Liebendörfer, Michael
AU - Schukajlow, Stanislaw
ID - 8564
IS - 3
JF - ZDM
SN - 1863-9690, 1863-9704
TI - Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?
VL - 49
ER -
TY - THES
AB - Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute
the set of optimal compromises (the Pareto set) between the conflicting objectives.
Since – in contrast to the solution of a single objective optimization problem – the
Pareto set generally consists of an infinite number of solutions, the computational
effort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives
are costly to evaluate. Consequently, this thesis is devoted to the identification and
exploitation of structure both in the Pareto set and the dynamics of the underlying
model as well as to the development of efficient algorithms for solving problems with
additional parameters, with a high number of objectives or with PDE-constraints.
These three challenges are addressed in three respective parts.
In the first part, predictor-corrector methods are extended to entire Pareto sets.
When certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent
space can be approximated numerically which yields a direction for the predictor
step. In the corrector step, the predicted set converges to the Pareto set at a new
parameter value. The resulting algorithm is applied to an example from autonomous
driving.
In the second part, the hierarchical structure of Pareto sets is investigated. When
considering a subset of the objectives, the resulting solution is a subset of the Pareto
set of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This
way, the “skeleton” of a Pareto set can be computed and due to the exponential
increase in computing time with the number of objectives, the computations of
these subsets are significantly faster which is demonstrated using an example from
industrial laundries.
In the third part, PDE-constrained multiobjective optimal control problems are
addressed by reduced order modeling methods. Reduced order models exploit the
structure in the system dynamics, for example by describing the dynamics of only the
most energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of
algorithms. Both scalarization and set-oriented approaches are coupled with reduced
order modeling. Convergence results are presented and the numerical benefit is
investigated. The algorithms are applied to semi-linear heat flow problems as well
as to the Navier-Stokes equations.
AU - Peitz, Sebastian
ID - 10594
TI - Exploiting structure in multiobjective optimization and optimal control
ER -
TY - CONF
AU - Göller, Robin
AU - Liebendörfer, Michael
ED - für Didaktik der Mathematik, Gesellschaft
ID - 8566
KW - \_tablet
KW - Abschreiben
T2 - Beiträge zum Mathematikunterricht 2016
TI - Eine alternative Einstiegsvorlesung in die Fachmathematik – Konzept und Auswirkungen
ER -
TY - CONF
AU - Schumacher, Jan
ID - 7765
T2 - Beiträge zum Mathematikunterricht 2016
TI - Erkunden mathematischer Strukturen anstatt Interpretation in Modellen – Ein innermathematischer Zugang zu negativen Zahlen
ER -
TY - CHAP
AU - Kolter, Jana
AU - Liebendörfer, Michael
AU - Schukajlow, Stanislaw
ED - Hoppenbrock, Axel
ED - Biehler, Rolf
ED - Hochmuth, Reinhard
ED - Rück, Hans-Georg
ID - 8555
SN - 978-3-658-10260-9 978-3-658-10261-6
T2 - Lehren und Lernen von Mathematik in der Studieneingangsphase
TI - Mathe – nein danke? Interesse, Beliefs und Lernstrategien im Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach
ER -
TY - CONF
AU - Colberg, Christoph
AU - Biehler, Rolf
AU - Hochmuth, Reinhard
AU - Schaper, Niclas
AU - Liebendörfer, Michael
AU - Schürmann, Mirko
ID - 8562
T2 - Beiträge zum Mathematikunterricht 2016
TI - Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase
ER -
TY - JOUR
AU - Liebendörfer, Michael
AU - Göller, Robin
ID - 8567
IS - 4
JF - Mitteilungen der Deutschen Mathematiker-Vereinigung
KW - \_tablet
KW - Abschreiben
TI - Abschreiben von Übungsaufgaben in traditionellen und innovativen Mathematikvorlesungen
VL - 24
ER -
TY - CONF
AB - In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intelligent cruise control in order to extend the vehicle range, i.e. to minimize energy consumption, by computing the optimal torque profile for a given track. On the one hand, a path-based linear model with strong simplifications regarding the vehicle dynamics is used. On the other hand, a nonlinear model is employed in which the dynamics of the mechanical and electrical subsystem are modeled.
AU - Eckstein, Julian
AU - Peitz, Sebastian
AU - Schäfer, Kai
AU - Friedel, Patrick
AU - Köhler, Ulrich
AU - Molo, Mirko Hessel-von
AU - Ober-Blöbaum, Sina
AU - Dellnitz, Michael
ID - 8758
SN - 2212-0173
T2 - Procedia Technology
TI - A Comparison of two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles
ER -
TY - THES
AB - Lightweight materials play an ever growing role in today's world. Saving on the mass of a machine will usually translate into a lower energy consumption. However, lightweight applications are prone to develop performance problems due to vibration induced by the operation of the machine. The Fraunhofer Institute for Manufacturing Technology and Advanced Materials in Dresden conducts research into the damping properties of composite materials. They are experimenting with hollow, particle filled spheres embedded in the lightweight material. Such a system is the technical motivation of this thesis. Ultimately, a numerical experiment to derive the coefficient of restitution is required. The simulation developed in this thesis is based on a discrete element method to track the individual particle and sphere trajectories. Based on a potential based approach for the particle interactions deployed in molecular dynamics, the behavior of the particles can be controlled effectively. The simulated volume is using reflecting boundaries and encloses the hollow sphere. In this work, a highly flexible memory structure was used with a linked cell approach to cope with the highly flexible mass of particles. This allows for a linear complexity of the method in regard to the particle number by reducing the computational overhead of the interaction computation. Multiple numerical experiments show the great effect the particles have on the damping behavior of the system.
AU - Steinle, Tobias
ID - 33
TI - Modeling and simulation of metallic, particle-damped spheres for lightweight materials
ER -
TY - CONF
AU - Jurgelucks, Benjamin
AU - Claes, Leander
ID - 6570
T2 - AD2016 The 7th International Conference on Algorithmic Differentiation
TI - Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation
ER -
TY - CONF
AB - In a wide range of applications, it is desirable to optimally control a system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario.
AU - Peitz, Sebastian
AU - Gräler, Manuel
AU - Henke, Christian
AU - Molo, Mirko Hessel-von
AU - Dellnitz, Michael
AU - Trächtler, Ansgar
ID - 8759
SN - 2212-0173
T2 - Procedia Technology
TI - Multiobjective Model Predictive Control of an Industrial Laundry
ER -
TY - CONF
AU - Dellnitz, Michael
AU - Eckstein, Julian
AU - Flaßkamp, Kathrin
AU - Friedel, Patrick
AU - Horenkamp, Christian
AU - Köhler, Ulrich
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
AU - Tiemeyer, Sebastian
ID - 34
SN - 2212-0173
T2 - Progress in Industrial Mathematics at ECMI
TI - Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control
VL - 22
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Göller, Robin
ED - Paravicini, Walther
ED - Schnieder, Jörn
ID - 8565
SN - 978-3-942197-99-1
T2 - Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2014 Beiträge zum gleichnamigen Symposium am 7. & 8. November 2014 an der Westfälischen Wilhelms-Universität Münster
TI - Abschreiben - ein Problem in mathematischen Lehrveranstaltungen?
ER -
TY - CHAP
AU - Colberg, Christoph
AU - Schürmann, Mirko
AU - Biehler, Rolf
AU - Hochmuth, Reinhard Karl
AU - Schaper, Niclas
AU - Liebendörfer, Michael
ED - Hanft, Anke
ED - Bischoff, Franziska
ED - Prang, Bianca
ID - 8558
T2 - Working Paper Studieneingangsphase Perspektiven aus der Begleitforschung zum Qualitätspakt Lehre
TI - Projekt WiGeMath: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase
ER -
TY - JOUR
AU - Biehler, Rolf
AU - Hochmuth, Reinhard
AU - Rück, Hans-Georg
AU - Göller, Robin
AU - Hoppenbrock, Axel
AU - Liebendörfer, Michael
AU - Püschl, Juliane
ID - 8560
IS - 102
JF - EMS Newsletter
SN - 1027-488X
TI - Research in University Mathematics Education: The khdm
VL - 12
ER -
TY - GEN
AU - Jurgelucks, Benjamin
AU - Claes, Leander
ID - 6569
T2 - 2nd Seminar on Ferroic Functional Materials & 12th International Workshop on Direct and Inverse Problems in Piezoelectricity
TI - Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation
ER -
TY - JOUR
AB - In this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 1774
IS - 1
JF - PAMM
SN - 1617-7061
TI - Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction
VL - 15
ER -
TY - JOUR
AB - Große zylindrische Stahlprüflinge werden mittels der Methode der finiten Differenzen im Zeitbereich (engl. finite differences in time domain, FDTD) simulativ untersucht. Dabei werden Pitch-Catch-Messanordnungen verwendet. Es werden zwei Bildgebungsansätze vorgestellt: ersterer basiert auf dem Imaging Principle nach Claerbout, letzterer basiert auf gradientenbasierter Optimierung eines Zielfunktionals.
AU - Hegler, Sebastian
AU - Statz, Christoph
AU - Mütze, Marco
AU - Mooshofer, Hubert
AU - Goldammer, Matthias
AU - Fendt, Karl
AU - Schwarzer, Stefan
AU - Feldhoff, Kim
AU - Flehmig, Martin
AU - Markwardt, Ulf
AU - E. Nagel, Wolfgang
AU - Schütte, Maria
AU - Walther, Andrea
AU - Meinel, Michael
AU - Basermann, Achim
AU - Plettemeier, Dirk
ID - 1769
IS - 9
JF - tm - Technisches Messen
TI - Simulative Ultraschall-Untersuchung von Pitch-Catch-Messanordnungen für große zylindrische Stahl-Prüflinge und gradientenbasierte Bildgebung
VL - 82
ER -
TY - CONF
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
ED - Krainer, Konrad
ED - Vondrová, Nad'a
ID - 8563
T2 - Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education
TI - Perceived Autonomy in the First Semester of Mathematics Studies
ER -
TY - JOUR
AU - Braun, Eileen Angélique
AU - Liebendörfer, Michael
AU - Schorcht, Sebastian
ID - 8568
IS - 98
JF - Mitteilungen der Gesellschaft für Didaktik der Mathematik
TI - Initiative Bottom-Up-Nachtreffen zum Doktorandenkolloquium der GDM
VL - 41
ER -
TY - CONF
AB - n this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 8760
SN - 1617-7061
T2 - PAMM
TI - Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction
ER -
TY - CONF
AB - In light of an increasing awareness of environmental challenges, extensive research is underway to develop new light-weight materials. A problem arising with these materials is their increased response to vibration. This can be solved using a new composite material that contains embedded hollow spheres that are partially filled with particles. Progress on the adaptation of molecular dynamics towards a particle-based numerical simulation of this material is reported. This includes the treatment of specific boundary conditions and the adaption of the force computation. First results are presented that showcase the damping properties of such particle-filled spheres in a bouncing experiment.
AU - Steinle, Tobias
AU - Vrabec, Jadran
AU - Walther, Andrea
ED - Bock, Hans Georg
ED - Hoang, Xuan Phu
ED - Rannacher, Rolf
ED - Schlöder, Johannes P.
ID - 1781
SN - 978-3-319-09063-4
T2 - Proc. Modeling, Simulation and Optimization of Complex Processes (HPSC)
TI - Numerical Simulation of the Damping Behavior of Particle-Filled Hollow Spheres
ER -
TY - CONF
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
AU - Kolter, Jana
AU - Schukajlow, Stanislaw
ED - Nicol, C.
ED - Oesterle, S.
ED - Liljedahl, Peter
ED - Allan, D.
ID - 8554
T2 - Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education an the 36th Conference of the North American Chapter of the Psychology of Mathematics Education
TI - The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers
VL - 6
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
AU - Schreiber, Stephan
AU - Göller, Robin
AU - Kolter, Jana
AU - Biehler, Rolf
AU - Kortemeyer, Jörg
AU - Ostsieker, Laura
ED - Roth, Jürgen
ED - Ames, J.
ID - 8561
T2 - Beiträge zum Mathematikunterricht 2014
TI - Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Ostsieker, Laura
ED - Wassong, Thomas
ED - Frischemeier, Daniel
ED - Fischer, Pascal R.
ED - Hochmuth, Reinhard
ED - Bender, Peter
ID - 8550
SN - 978-3-658-03103-9 978-3-658-03104-6
T2 - Mit Werkzeugen Mathematik und Stochastik lernen – Using Tools for Learning Mathematics and Statistics
TI - Mathematik als Werkzeug: Sicht- und Arbeitsweisen von Studierenden am Anfang ihres Mathematikstudiums
ER -
TY - JOUR
AU - Liebendörfer, Michael
ID - 8557
IS - 4
JF - Oberwolfach Reports
TI - Self-determination and interest development of first-year mathematics students
VL - 11
ER -
TY - CONF
AB - In this contribution, the range extension problem of electric vehicles is addressed. To this aim, an intelligent cruise control is developed based on the formulation of an optimal control problem. Solutions of this optimal control problem are energy efficient accelerator pedal position profiles. They can be computed numerically by a direct optimal control method using sequential quadratic programming. The approach is applied to two different driving scenarios. The results show that the energy efficiency is increased by using optimal control for both an artificial and a realistic scenario.
AU - Dellnitz, Michael
AU - Eckstein, Julian
AU - Flaßkamp, Kathrin
AU - Friedel, Patrick
AU - Horenkamp, Christian
AU - Köhler, Ulrich
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
AU - Tiemeyer, Sebastian
ID - 8761
SN - 2212-0173
T2 - Procedia Technology
TI - Development of an Intelligent Cruise Control Using Optimal Control Methods
VL - 15
ER -
TY - CHAP
AU - Göller, Robin
AU - Kortemeyer, Jörg
AU - Liebendörfer, Michael
AU - Biehler, Rolf
AU - Hochmuth, Reinhard
AU - Krämer, Jana
AU - Ostsieker, Laura
AU - Schreiber, Stephan
ED - Greefrath, Gilbert
ID - 8547
T2 - Beiträge zum Mathematikunterricht 2013: Vorträge auf der 47. Tagung für Didaktik der Mathematik
TI - Instrumentenentwicklung zur Messung von Lernstrategien in mathematikhaltigen Studiengängen
ER -
TY - CHAP
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
ED - Lindmeier, Anke
ED - Heinze, Aiso
ID - 8551
T2 - Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education
TI - Interest and Self-Determination in the Transition to Studying Mathematics
VL - 5
ER -
TY - CONF
AU - Kolter, Jana
AU - Liebendörfer, Michael
ID - 8549
T2 - Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr
TI - Mathe – nein danke? Interesse im und am Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach
ER -
TY - CONF
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
ED - Ubuz, Behiye
ED - Haser, Çiğdem}
ED - Mariotti, Maria Alessandra
ID - 8553
SN - 978-975-429-315-9
T2 - Proceedings of the 8th {Conference} of European Research in Mathematics Education
TI - Interest in Mathematics and the First Steps at the University
ER -
TY - CONF
AB -
Paper Abstract
High harmonic generation is investigated for a two-band model of a semiconductor nanostructure. Similar to an atomic two-level system, the semiconductor emits high harmonic radiation. We show how one can specifically enhance the emission for a given frequency by applying a non-trivially shaped laser pulse. Therefore, the semiconductor Bloch equations including the interband and additionally the intraband dynamics are solved numerically and the spectral shape of the input pulse is computed via an optimization algorithm. It is demonstrated that desired emission frequencies can be favored even though the overall input power is kept constant. We also suggest special metallic nano geometries to achieve enhanced localized optical fields. They are found by geometric optimization.
AU - Reichelt, Matthias
AU - Hildebrandt, Andre
AU - Walther, Andrea
AU - Förstner, Jens
AU - Meier, Torsten
ID - 3980
KW - tet_topic_shg
SN - 9780819489036
T2 - Ultrafast Phenomena and Nanophotonics XVI
TI - Engineering high harmonic generation in semiconductors via pulse shaping
ER -
TY - CONF
AU - Liebendörfer, Michael
AU - Hochmuth, Reinhard
ID - 8548
T2 - Beiträge zum Mathematikunterricht 2012 : Vorträge auf der 46. Tagung für Didaktik der Mathematik
TI - Mathematikinteresse im 1. Studiensemester
VL - 1
ER -
TY - JOUR
AB - We consider the space of complete rank two collineations. Starting from its description as a limit of GIT-quotients of a Grassmanian G(2, n) by a certain {\textbackslash}documentclass\{article\}{\textbackslash}usepackage\{amssymb\}{\textbackslash}begin\{document\}{\textbackslash}pagestyle\{empty\}\${\textbackslash}mathbb \{C\}{\textasciicircum}*\${\textbackslash}end\{document\}-action, we determine the Cox ring by means of toric ambient modifications.
AU - Hausen, Jürgen
AU - Liebendörfer, Michael
ID - 8556
IS - 8-9
JF - Mathematische Nachrichten
SN - 1522-2616
TI - The Cox ring of the space of complete rank two collineations
VL - 285
ER -
TY - CONF
AU - Biehler, Rolf
AU - Hoppenbrock, Axel
AU - Klemm, Juliane
AU - Liebendörfer, Michael
AU - Wassong, Thomas
ID - 8552
T2 - CETL-MSOR Conference 2011
TI - Training of student teaching assistants and e-learning via math-bridge – Two projects at the German Centre for Higher Mathematics Education
ER -
TY - JOUR
AU - Steffen, Eckhard
ID - 10171
JF - Discrete Mathematics
TI - Nearly nowhere-zero r-flow graphs
VL - 312
ER -