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Real-Time PDE-Constrained OptimizationReal-Time PDE-Constrained Optimization

Edited by Lorenz T. Biegler, Omar Ghattas, Matthias Heinkenschloss, David Keyes, and Bart van Bloemen Waanders

Computational Science and Engineering 3

Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs—and the requirement for rapid solution—pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making.

Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics.

Despite difficulties, there is a pressing need to capitalize on continuing advances in computing power to develop optimization methods that will replace simple rule-based decision making with optimized decisions based on complex PDE simulations.

The book is aimed at readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in “offline” optimization contexts and are interested in moving to “online” optimization.

Table of Contents [PDF 264KB]
Preface [PDF 278KB]
Index [PDF 232KB]

About the Authors
Lorenz T. Biegler is the Bayer Professor of Chemical Engineering at Carnegie Mellon University. His research interests are in the development and application of concepts in optimization theory, operations research, and numerical methods for process design, analysis, and control.
Omar Ghattas is the John A. and Katherine G. Jackson Chair in Computational Geosciences at the University of Texas at Austin. His research focuses on optimization, parameter estimation, and uncertainty quantification for large-scale problems in the geological, mechanical, and biomedical engineering sciences.
Matthias Heinkenschloss is Professor of Computational and Applied Mathematics at Rice University. His research interests are in numerical solution of large-scale optimization, optimal control, and parameter identification problems; domain decomposition methods; preconditioning of KKT systems; error estimation for optimal control problems; and applications in science and engineering.
David E. Keyes is the Fu Foundation Professor of Applied Mathematics at Columbia University. He works at the algorithmic interface between parallel computing and the numerical analysis of partial differential equations, across a spectrum of aerodynamic, geophysical, and chemically reacting flows.
Bart van Bloemen Waanders is Principal Member of the Technical Staff at Sandia National Laboratories. His main area of research is the development, analysis, and application of methods for PDE-constrained optimization, especially for large state and design spaces, including inverse problems, shape optimization, and design problems.

2007 / xxiv + 312 pages / Softcover
ISBN: 978-0898716-21-4
List Price $105.50 / SIAM Member Price $73.85 / Order Code CS03
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)