Numerical PDE-Constrained Optimization
This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their applic
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pringerBriefs in Optimization showcase algorithmic and theoretical techniques, case studies, and applications within the broad-based field of optimization. Manuscripts related to the ever-growing applications of optimization in applied mathematics, engineering, medicine, economics, and other applied sciences are encouraged.
For further volumes: http://www.springer.com/series/8918
Juan Carlos De los Reyes
Numerical PDE-Constrained Optimization
Juan Carlos De los Reyes Centro de Modelizaci´on Matem´atica (MODEMAT) and Department of Mathematics Escuela Polit´ecnica Nacional Quito Quito Ecuador
ISSN 2190-8354 SpringerBriefs in Optimization ISBN 978-3-319-13394-2 DOI 10.1007/978-3-319-13395-9
ISSN 2191-575X (electronic) ISBN 978-3-319-13395-9 (eBook)
Library of Congress Control Number: 2014956766 Mathematics Subject Classification (2010): 49K20, 49K21, 49J20, 49J21, 49M05, 49M15, 49M37, 65K10, 65K15, 35J25, 35J60, 35J86. Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Mar´ıa Soledad and Esteban
Preface
In recent years, the field of partial differential equation (PDE)-constrained optimization has received a significant impulse with large research projects being funded by different national and international agencies. A key ingredient for this success is related to the wide applicability that the developed results have (e.g., in crystal growth, fluid flow, or heat phenomena). In return, application problems gave rise to further deep theoretical and numerical developments. In particular, the numerical treatment of such problems has motivated the design of efficient computational methods in order to obtain optimal solutions in a manageable amount of time. Although some books on optimal control of PDEs have been edited in the past years, they are mainly concentrated on theoretical aspects or on research
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