Optimal Control of Partial Differential Equations - Manzoni, Andrea

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Résumé :
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 ofOCPs 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.

Biographie:
Prof. Alfio Quarteroni, Dr. Andrea Manzoni and Federico Negri - Ecole Polytechnique F?d?rale de Lausanne, Lausanne, Switzerland....

Sommaire:
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.