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.