Exploiting structure in multiobjective optimization and optimal control / von Sebastian Peitz ; [Gutachter: Prof. Dr. Michael Dellnitz, Prof. Dr. Sina Ober-Blöbaum, Prof. Dr. Stefan Volkwein]. Paderborn, 2017
Content
- Introduction
- Theoretical Background
- Multiobjective Optimization
- Pareto Optimality
- Gradients and Descent Directions in Multiobjective Optimization
- Manifold Conditions for Pareto Sets
- Solution Methods
- The Subdivision Algorithm
- Optimal Control and Model Predictive Control
- Reduced Order Modeling
- Continuation of Parameter Dependent Pareto Sets
- Multiobjective Model Predictive Control of Electric Vehicles
- Multiobjective Optimal Control of Electric Vehicles
- The Offline-Online Multiobjective MPC Concept
- Results
- Continuation of Pareto Sets
- Application to Autonomous Driving
- Solving Many-Objective Optimization Problems via Subsets of Objectives
- The Hierarchical Structure of Pareto Sets
- A Multiobjective Extension of the -Constraint Method
- Numerical Examples
- Application: Industrial Laundry
- Multiobjective Optimal Control of PDEs Using Reduced Order Modeling
- Multiobjective Optimal Control of the Navier-Stokes Equations
- Problem Formulation
- Numerical discretization
- Multiobjective optimal control problem
- Reduced Order Model
- Adjoint Systems
- Results
- A Trust-Region Algorithm for MOC of Nonlinear PDEs
- Extension of the Subdivision Algorithm to Inexact Models
- Problem setting
- Descent Directions in the Presence of Inexactness
- Extension of the Subdivision Algorithm to Inexact Gradients
- Examples
- Set-Oriented Multiobjective Optimal Control of PDEs using ROMs
- Conclusion and Outlook
- Continuation of Parameter Dependent Pareto Sets
- Solving Many-Objective Optimization Problems via Subsets of Objectives
- Multiobjective Optimal Control of PDEs Using Reduced Order Modeling
- Future Work
- Bibliography