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
Inhalt
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