This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs). As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. We place special emphasis on algorithm development and numerical computation. The second part of this volume focuses on the application of PDE-constrained optimization including problems in optimal control, optimal design and inverse problems, which includes a comprehensive treatment of inverse problems arising in the oil and gas industry, among other topics. Read more...
Abstract:
The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Read more...
Author(s): Antil, Harbir; Kouri, Drew P.; Lacasse, Martin-D.; Ridzal, Denis et al. (eds.)
Series: IMA volumes in mathematics and its applications 163
Publisher: Springer
Year: 2018
Language: English
Pages: 435
City: Minneapolis, Minnesota
Tags: Constrained optimization -- Congresses.;Differential equations, Partial -- Congresses.;MATHEMATICS / Applied.;MATHEMATICS / Probability & Statistics / General.;Applied mathematics.;Optimization.;Topology.;Differential calculus & equations.;Constrained optimization.;Differential equations, Partial.;Partial Differential Equations.;Mathematics of Planet Earth.
Content: Part I: PDE-Constrained Optimization --
Tutorials --
A Brief Introduction to PDE Constrained Optimization --
Optimization of PDEs with Uncertain Inputs --
Inexact Trust-Region Methods for PDE-Constrained Optimization --
Numerical Optimization Methods for the Optimal Control of Elliptic Inequalities --
Introduction to PDE-Constrained Optimization in the Oil and Gas Industry --
An Extreme-Scale PDE-Constrained Optimization Problem --
Part II: PDE-Constrained Optimization --
Applications --
Energetically Optimal Flapping Wing Motions via Adjoint-Based Optimization and High-Order Discretizations --
Optimization of a Fractional Differential Equation --
Sensitivity-Based Topology and Shape Optimization with Electric Motors --
Distributed Parameter Estimation for the Time-Dependent Radiative Transfer Equation --
On the Use of Optimal Transport Distances for a PDE-Constrained Optimization Problem in Seismic Imaging --
Exploiting Sparsity in Solving PDE-Constrained Inverse Problems: Application to Subsurface Flow Model Calibration.
