Control and Optimization with PDE Constraints

✍ Scribed by Alessandro Alla, Maurizio Falcone (auth.), Kristian Bredies, Christian Clason, Karl Kunisch, Gregory von Winckel (eds.)

• Publisher: Birkhäuser Basel
• Year: 2013
• Tongue: English
• Leaves: 221
• Series: International Series of Numerical Mathematics 164
• Edition: 1
• Category: Library

✦ Synopsis

Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.

✦ Table of Contents

Front Matter....Pages I-X
An Adaptive POD Approximation Method for the Control of Advection-Diffusion Equations....Pages 1-17
Generalized Sensitivity Analysis for Delay Differential Equations....Pages 19-44
Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives....Pages 45-55
Nonsmooth Optimization Method and Sparsity....Pages 57-77
Parareal in Time Intermediate Targets Methods for Optimal Control Problems....Pages 79-92
Hamilton–Jacobi–Bellman Equations on Multi-domains....Pages 93-116
Gradient Computation for Model Calibration with Pointwise Observations....Pages 117-136
Numerical Analysis of POD A-posteriori Error Estimation for Optimal Control....Pages 137-158
Cubature on C 1 Space....Pages 159-172
A Globalized Newton Method for the Optimal Control of Fermionic Systems....Pages 173-191
A Priori Error Estimates for Optimal Control Problems with Constraints on the Gradient of the State on Nonsmooth Polygonal Domains....Pages 193-215

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Calculus of Variations and Optimal Control; Optimization; Numerical Analysis