Numerical PDE-Constrained Optimization

1. Front Matter

   Pages i-x

   PDF

2. Introduction

   • Juan Carlos De los Reyes

   Pages 1-8

3. Basic Theory of Partial Differential Equations and Their Discretization

   • Juan Carlos De los Reyes

   Pages 9-23

4. Theory of PDE-Constrained Optimization

   • Juan Carlos De los Reyes

   Pages 25-41

5. Numerical Optimization Methods

   • Juan Carlos De los Reyes

   Pages 43-68

6. Box-Constrained Problems

   • Juan Carlos De los Reyes

   Pages 69-90

7. Nonsmooth PDE-Constrained Optimization

   • Juan Carlos De los Reyes

   Pages 91-118

8. Back Matter

   Pages 119-123

   PDF

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.

• Numerical optimization
• Optimal control
• Optimality conditions
• Optimization methods
• PDE-constrained optimization
• partial differential equations

• Escuela Politécnica Nacional Quito, Quito, Ecuador

  Juan Carlos De los Reyes

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.

Policies and ethics