274 citations · 1k across the 43 of their papers we have counts for
25 papers · 1 filter
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
Konstantin Sonntag, Bennet Gebken, Georg Müller +2
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spa…
Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
Marco Bernreuther, Michael Dellnitz, Bennet Gebken +4
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimizati…
Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping
Konstantin Sonntag, Sebastian Peitz
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping.…
Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients
Manuel Berkemeier, Sebastian Peitz
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogat…
Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-like Systems
Konstantin Sonntag, Sebastian Peitz
We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To th…
Towards reliable data-based optimal and predictive control using extended DMD
Manuel Schaller, Karl Worthmann, Friedrich Philipp +2
While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates…
On the structure of regularization paths for piecewise differentiable regularization terms
Bennet Gebken, Katharina Bieker, Sebastian Peitz
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity.…
Finite-data error bounds for Koopman-based prediction and control
Feliks Nüske, Sebastian Peitz, Friedrich Philipp +2
The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularit…
Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
Manuel Berkemeier, Sebastian Peitz
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive…
On the Universal Transformation of Data-Driven Models to Control Systems
Sebastian Peitz, Katharina Bieker
The advances in data science and machine learning have resulted in significant improvements regarding the modeling and simulation of nonlinear dynamical systems. It is nowadays pos…
On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
Katharina Bieker, Bennet Gebken, Sebastian Peitz
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scienti…
An efficient descent method for locally Lipschitz multiobjective optimization problems
Bennet Gebken, Sebastian Peitz
In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoreti…
Data-Driven Model Predictive Control using Interpolated Koopman Generators
Sebastian Peitz, Samuel E. Otto, Clarence W. Rowley
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserv…
Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty
Carlos Ignacio Hernández Castellanos, Sina Ober-Blöbaum, Sebastian Peitz
In real-world problems, uncertainties (e.g., errors in the measurement, precision errors) often lead to poor performance of numerical algorithms when not explicitly taken into acco…
ROM-based multiobjective optimization of elliptic PDEs via numerical continuation
Stefan Banholzer, Bennet Gebken, Michael Dellnitz +2
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimiza…
Inverse multiobjective optimization: Inferring decision criteria from data
Bennet Gebken, Sebastian Peitz
It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and…
Explicit multiobjective model predictive control for nonlinear systems with symmetries
Sina Ober-Blöbaum, Sebastian Peitz
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 mo…
Feedback control of nonlinear PDEs using data-efficient reduced order models based on the Koopman operator
Sebastian Peitz, Stefan Klus
In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linea…
Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives
Sören Hanke, Sebastian Peitz, Oliver Wallscheid +3
Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.…
On the hierarchical structure of Pareto critical sets
Bennet Gebken, Sebastian Peitz, Michael Dellnitz
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems…
Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data
Sebastian Peitz
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 switche…
A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems
Bennet Gebken, Sebastian Peitz, Michael Dellnitz
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for un…
Gradient-Based Multiobjective Optimization with Uncertainties
Sebastian Peitz, Michael Dellnitz
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 f…
A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles
Sebastian Peitz, Kai Schäfer, Sina Ober-Blöbaum +3
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 o…