Mathematical Modelling: Theory and Applications

Optimization with PDE Constraints

Authors: Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.

  • Concise functional analytic setting for pde constrained optimization problems
  • Modern infinite-dimensional tailored algorithmical framework
  • Structure exploiting, problem adapted discrete treatment of pdes and constraints
  • Challenging applications
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Hardcover $119.00
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  • ISBN 978-1-4020-8838-4
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Softcover $119.00
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About this book

This book presents a modern introduction of pde constrained optimization. It provides a precise functional analytic treatment via optimality conditions and a state-of-the-art, non-smooth algorithmical framework. Furthermore, new structure-exploiting discrete concepts and large scale, practically relevant applications are presented. The main focus is on the algorithmical and numerical treatment of pde constrained optimization problems on the infinite dimensional level. A particular emphasis is on simple constraints, such as pointwise bounds on controls and states. For these practically important situations, tailored Newton- and SQP-type solution algorithms are proposed and a general convergence framework is developed. This is complemented with the numerical analysis of structure-preserving Galerkin schemes for optimization problems with elliptic and parabolic equations. Finally, along with the optimization of semiconductor devices and the optimization of glass cooling processes, two challenging applications of pde constrained optimization are presented. They demonstrate the scope of this emerging research field for future engineering applications.

Reviews

From the reviews:

"The book presents a state-of-the-art of optimization problems described by partial differential equations (PDEs) and algorithms for obtaining their solutions. Solving optimization problems with constraints given in terms of PDEs is one of the most challenging problems appearing, e.g., in industry, medical and economical applications. The book consists of four chapters. … This well-written book can be recommended to scientists and graduate students working in the fields of optimal control theory, optimization algorithms and numerical solving of optimization problems described by PDEs." (Wieslaw Kotarski, Zentralblatt MATH, Vol. 1167, 2009)


Table of contents (4 chapters)

  • Analytical Background and Optimality Theory

    Ulbrich, Stefan

    Pages 1-95

  • Optimization Methods in Banach Spaces

    Ulbrich, Michael

    Pages 97-156

  • Discrete Concepts in PDE Constrained Optimization

    Hinze, Michael

    Pages 157-232

  • Applications

    Pinnau, René

    Pages 233-263

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4020-8839-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-4020-8838-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-90-481-8003-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optimization with PDE Constraints
Authors
Series Title
Mathematical Modelling: Theory and Applications
Series Volume
23
Copyright
2009
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-8839-1
DOI
10.1007/978-1-4020-8839-1
Hardcover ISBN
978-1-4020-8838-4
Softcover ISBN
978-90-481-8003-5
Series ISSN
1386-2960
Edition Number
1
Number of Pages
XII, 270
Topics