Optimization and Control for Partial Differential Equations

Uncertainty quantification, open and closed-loop control, and shape optimization

Roland Herzog, Matthias Heinkenschloss, Dante Kalise, Georg Stadler, Emmanuel Trélat, Roland Herzog, Matthias Heinkenschloss, Dante Kalise, Georg Stadler, Emmanuel Trélat

• Publisher: De Gruyter
• Year: 2022
• eBook ISBN: 9783110696004
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Table of contents

• Title Page
• Copyright
• Contents
• 1 Reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE
• 2 Pointwise moving control for the 1-D wave equation Numerical approximation and optimization of the support
• 3 Limits of stabilizability for a semilinear model for gas pipeline flow
• 4 Minimal cost-time strategies for mosquito population replacement
• 5 The sterile insect technique used as a barrier control against reinfestation
• 6 Variational discretization approach applied to an optimal control problem with bounded measure controls
• 7 An optimal control problem for equations with p-structure and its finite element discretization
• 8 Unstructured space-time finite element methods for optimal sparse control of parabolic equations
• 9 An adaptive finite element approach for lifted branched transport problems
• 10 High-order homogenization of the Poisson equation in a perforated periodic domain
• 11 Least-squares approaches for the 2D Navier–Stokes system
• 12 Numerical issues and turnpike phenomenon in optimal shape design
• 13 Feedback stabilization of Cahn–Hilliard phase-field systems
• 14 Ensemble Kalman filter for neural network-based one-shot inversion
• 15 Deep learning in high dimension: ReLU neural network expression for Bayesian PDE inversion
• Subject Index