Master Theses in Nonlinear Optimization
The topics of Master Theses in nonlinear optimization are in general related to specific applications or deal with analytical questions regarding optimization. Depending on the topic and preferences, the thesis includes scientific aspects from numerics, analysis, partial differential equations or stochastics. Typically, the topic covers specific tasks of ongoing projects from mathematical research collaborations as well as projects with engineers or industrial partners.
The application of a thesis is as follows. In an initial meeting Prof. Ulbrich discuss possible topics of your thesis with you. Thereby suggestions and preferences of your research interests can be taken into account. Afterwards you have four to six weeks to get familiar with the topic and to complete the literature research. Then you and your supervisor define jointly the aim, the organizational process and the schedule of your work in connection with official notification of the Examination Secretariat. During writing your thesis your supervisor or a research assistant is available to answer your questions.
Requirements
Passing one of the exams “Introduction of Optimization”, “Discrete Optimization” or “Nonlinear Optimization” gives you the prerequisite for writing a thesis in our group. In addition, it is highly recommended to participate at an optimization seminar. Programming knowledge is advisable.
Contact
Prof. Ulbrich and staff members of the research group
- Universal adversarial perturbations
(Prof. Ulbrich) - Modelling and Optimization of a Dynamic Truck network for Daily Sales and Supply Operations under Stochastic Demand
(Prof. Ulbrich)
- Sparse semismooth Newton methods for the clustered Lasso problem
(Prof. Ulbrich) - A Linearly Convergent Regularized Proximal Point Algorithm for Fused Multiple Graphical Lasso Problems
(Prof. Ulbrich) - Robust Optimization for Adversarial Deep Learning
(Prof. Ulbrich)
- Gradient calculation for the yield function
(Prof. Wollner)
- Bayesian Inverse problems and the application on local volatility surfaces
(Prof. Wollner) - Relative Robust Portfolio Optimization, a Comparison of two Approaches
(Prof. Ulbrich) - Inexact solution in mixed integer optimization
(Prof. Wollner) - A non-smooth Trust-Region Method for locally Lipschitz Functions with Application to the Obstacle Problem
(Prof. Wollner) - Stochastic proximal gradient algorithm and application on non-convex PDE constrained optimization
(Prof. Wollner) - Stochastic Gradient Method and Inverse Problems
(Prof. Wollner) - Damage identification with non-smooth cost function
(Prof. Wollner) - Efficient usage of Attention in U-Nets for medical image segmentation
(Prof. Ulbrich) - Stochastic Optimization of Multi-Stage Supply-Chain Problems under Demand Uncertainty
(Prof. Wollner) - Initial-boundary value problem for a scalar hyberbolic conservation law with node condition
(Prof. Ulbrich) - Trust Region Policy Optimization and related methods
(Prof. Ulbrich)
- Identification of Model Uncertainty via Optimal Design of Experiments by a Bayesian Approval
(Prof. Ulbrich) - Sequential quadratic programming for degenerate optimization problems in function spaces
(Prof. Wollner) - An Optimal Control Problem for the p-Laplace Equation
(Prof. Wollner) - Stochastic Gradient Methods for non convex PDE Constrained Optimization
(Prof. Wollner) - Optimization with PDEs and applications to identification of material damage
(Prof. Wollner) - Globale Optimierung gemischt-ganzzahliger Netzwerkprobleme mit DGL-Beschränkungen am Beispiel von Fernwärmenetzwerken
(Prof. Ulbrich)
- Optimization Problems with Complementary Constraints in the Context of Inverse Optional Control for Locomotion
(Prof. Ulbrich) - Decentralized Collaborative Learning of Personalized Models over Networks and Applications
(Prof. Ulbrich) - Stochastic Quasi-Newton methods for optimization problems in machine learning and comparison with first order methods
(Prof. Ulbrich) - A robust optimization approach for nonconvex machine learning problems
(Prof. Ulbrich) - A stochastic semismooth Newton method for nonsmooth nonconvex optimization
(Prof. Ulbrich) - A theoretical and computational analysis of the Lemke-Howson method for binatrix games
(Prof. Schwartz) - The stochastic gradient method and its application on PDE-constrained optimization
(Prof. Wollner)
- Lokales SQP-Verfahren bei Optimierungsproblemen mit Gleichgewichtsnebenbedingungen
(Prof. Wollner) - Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints
(Prof. Wollner) - Innere-Punkte-Verfahren in der Topologieoptimierung
(Prof. Wollner) - Ein exponentielles Relaxierungsverfahren für kardinalitätsrestringierte Optimierungsprobleme
(Prof. Schwartz) - SQP-Methods in topology optimization
(Prof. Wollner) - Trust-Region methods for optimization under uncertainty
(Prof. Wollner) - Stochastic approximation in non-convex optimization
(Prof. Wollner) - ADMM and Augmented ADMM for the Lasso Problem
(Prof. Ulbrich) - Parallel Methods for Machine Learning
(Prof. Ulbrich) - Stochastic gradient methods for neural networks
(Prof. Ulbrich) - Convergence analysis of a Sequential Response Surface Method
(Prof. Ulbrich) - Development of algorithms for individualized order assignment in manual order picking
(Prof. Ulbrich) - Convex relaxations of ODE-constraints in mixed-integer nonlinear optimization
(Prof. Ulbrich) - A deep structured learning approach for system identification
(Prof. Ulbrich) - Konvex-konkave Dekompositionsmethoden für nichtlinear semidefinite Programme mit Anwendung auf aktive Stabwerke
(Prof. Ulbrich) - Inexact bundle methods for shape optimization with elastic contact problems
(Prof. Ulbrich) - Shape optimization with a level set method
(Prof. Ulbrich) - Verschwindende Viskosität für die gradientenbasierte optimale Steuerung von skalaren Erhaltungsgleichungen
(Prof. Ulbrich) - Proximal Stochastic Coordinate Descent Methods
(Prof. Ulbrich) - Konstruktion konvexer Relaxationen für die Optimierung von Gastransporten mit Spatial Branching
(Prof. Ulbrich) - Optimization Methods for Deep Learning
(Prof. Ulbrich) - Training Neuronaler Netze mit Stochastischen Abstiegsverfahren
(Prof. Ulbrich) - Sequential Convex Programming with Application to Robust Truss Topology Design
(Prof. Ulbrich) - Mathematical programs with vanishing constraints and application to topology optimization
(Prof. Wollner) - Theoretischer und numerischer Vergleich der augmentierten Lagrange-Methode mit allgemeinen Penalty- und SQP-Verfahren
(Prof. Schwartz) - Robust Growth-Optimal Portfolios
(Prof. Ulbrich) - Gradient methods in Banach spaces
(Prof. Wollner) - Stochastic optimization in technical and operations planning of multimodal and road freight transportation
(Prof. Ulbrich)
- Shape optimization with a level set method
(Prof. Ulbrich) - Proximale stochastische koordinatenweise Abstiegsverfahren
(Prof. Ulbrich) - Gültige Relaxierungen der Eulergleichungen durch Diskretisierung zur Lösung von Zulässigkeitsproblemen in der Gasnetzwerkoptimierung
(Prof. Ulbrich) - Konvergenzanalyse des Multi-Block ADMM ohne strenge Konvexität, dessen Varianten und vergleichbare Algorithmen in der strukturierten konvexen Optimierung
(Prof. Ulbrich) - Numerische Behandlung von Optimalsteuerungsproblemen für skalare hyperbolische Erhaltungsgleichungen mit an-/aus-Schaltungen mit Anwendung auf Verkehrsmodelle mit Ampelschaltungen
(Prof. Ulbrich) - Kreditrisiko-Optimierung basierend auf dem Conditional Value-at-Risk
(Prof. Ulbrich) - Zur Portfolio-Auswahl unter Verteilungsunsicherheit: Ein robuster CVaR-Ansatz
(Prof. Ulbrich) - Reduzierte Modelle zur Zustandsschätzung in Advektions-Diffusions-Gleichungen
(Prof. Ulbrich) - Stochastische Gradientenverfahren im Kontext des maschinellen Lernens
(Prof. Ulbrich) - Nichtlineare robuste Optimierung via Sequential Convex Bilevel Programming
(Prof. Ulbrich) - Portfolio-Optimierung unter Verteilungsunsicherheit: Ein robuster CVaR-Ansatz
(Prof. Ulbrich) - Learning to Sample
(Prof. Wollner) - Optimierungsmethoden für die Seismische Inversion
(Prof. Wollner) - Optimales Experimentendesign für endlichdimensionale nichtlineare Bayesian Probleme
(Prof. Wollner) - Diskretisierung quasilinearer Optimierungsprobleme mit Zustandsschranken
(Prof. Wollner) - A Reformulation of Cardinality Constrained Optimization Problems with Semi-continuous Variables
- (Prof. Schwartz)
- Design Centering mit Anwendungen in der Hochfrequenzsimulation
(Prof. Schwartz) - Relaxed Constant Rank und verwandte Constraint Qualifications für nichtlineare Programme und Programme mit Gleichgewichtsrestriktionen
(Prof. Schwartz) - Ein mehrseitiges Relaxierungsverfahren für Optimierungsprobleme mit Kardinalitätsrestriktionen
(Prof. Schwartz) - Evaluation of Server Data with Machine Learning
(Prof. Schwartz) - Free Route and Airspace Restrictions
(Prof. Schwartz) - Stabilität optimaler Portfolios
(Prof. Schwartz)
