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.

Clear exposition of first and second order optimality conditions for PDE-constrained optimization problems Careful and accessible presentation of optimization methods for solving PDE-constrained optimization problems, including MATLAB codes Analytical and numerical treatment of representative nonsmooth PDE-constrained optimization problems Includes supplementary material: sn.pub/extras

Autorentext

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.

Inhalt
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.