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.
