Optimal control of partial differential equations : analysis, approximation, and applications / Andrea Manzoni, Alfio Quarteroni, Sandro Salsa.

Manzoni, Andrea [Browse]
  • Cham, Switzerland : Springer, [2021]
  • ©2021
xvii, 498 pages : illustrations (some color) ; 26 cm.


  • Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 207. [More in this series]
  • Applied mathematical sciences, 0066-5452 ; volume 207
Summary note
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--back cover.
Bibliographic references
Includes bibliographical references (pages 483-492) and index.
  • I. 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
  • References
  • Index.
  • 9783030772253 (hardcover)
  • 303077225X (hardcover)
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