Numerical PDE-Constrained Optimization

✍ Scribed by Juan Carlos De los Reyes (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 129
• Series: SpringerBriefs in Optimization
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-8
Basic Theory of Partial Differential Equations and Their Discretization....Pages 9-23
Theory of PDE-Constrained Optimization....Pages 25-41
Numerical Optimization Methods....Pages 43-68
Box-Constrained Problems....Pages 69-90
Nonsmooth PDE-Constrained Optimization....Pages 91-118
Back Matter....Pages 119-123

✦ Subjects

Optimization; Partial Differential Equations; Numerical Analysis