Numerical PDE-Constrained Optimization

2015
ISBN: 978-3-319-13394-2
Verlag: Springer International Publishing

Buch, Englisch, 123 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2175 g

Reihe: SpringerBriefs in 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 application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Zielgruppe

Research

Autoren/Hrsg.

De Los Reyes, Juan Carlos

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

Introduction.- Basic Theory of Partial Differential Equations and Their Discretization.- Theory of PDE-constrained Optimization.- Numerical Optimization Methods.- Box-constrained Problems.- Nonsmooth PDE-constrained Optimization.

Über Autor(innen)

Juan Carlos De los Reyes is a Director of the Research Center on Mathematical Modelling (MODEMAT), and Professor of Optimization and Control at Escuela Politecnica Nacional.