Optimal control of partial differential equations : analysis, approximation, and applications / Andrea Manzoni, Alfio Quarteroni, Sandro Salsa.
Manzoni, Andrea, author.; Quarteroni, Alfio, author.; Salsa, S., author.
2021
QA377
Available Online

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Title Optimal control of partial differential equations : analysis, approximation, and applications / Andrea Manzoni, Alfio Quarteroni, Sandro Salsa.
Author Manzoni, Andrea, author.
ISBN 9783030772260 (electronic bk.)
3030772268 (electronic bk.)
9783030772253 (print)
303077225X
DOI https://doi.org/10.1007/978-3-030-77226-0
Published Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource (xvii, 498 pages) : illustrations (some color).
Other Standard Identifiers 10.1007/978-3-030-77226-0 doi
Call Number QA377
Dewey Decimal Classification 515/.353
Summary This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a "hands-on' treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed January 4, 2022).
Added Author Quarteroni, Alfio, author.
Salsa, S., author.
Series Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 207. 2196-968X
Available in Other Form Print version: 9783030772253
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1 Introduction: Representative Examples, Mathematical Structure
Part I A Preview on Optimization and Control in Finite Dimensions
2 Prelude on Optimization: Finite Dimension Spaces
3 Algorithms for Numerical Optimization
4 Prelude on Control: The Case of Algebraic and ODE Systems
Part II Linear-Quadratic Optimal Control Problems
5 Quadratic control problems governed by linear elliptic PDEs
6 Numerical Approximation of Linear-Quadratic OCPs
7 Quadratic Control Problems Governed by Linear Evolution PDEs
8 Numerical Approximation of Quadratic OCPs Governed by Linear Evolution PDEs
Part III More general PDE-constrained optimization problems
9 A Mathematical Framework for Nonlinear OCPs
10 Advanced Selected Applications
11 Shape Optimization Problems
Appendix A Toolbox of Functional Analysis
Appendix B Toolbox of Numerical Analysis.

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