Optimization and Differentiation

The celebrated book of J.L. Lions “Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles” was published about half a century ago. It was the standard of the optimization control theory for the infinite dimensional systems. This book is an introduction to optimization control theory for the systems described by nonlinear partial differential equations. It discusses the interpretation of this theory as an application of the differentiation theory. A lot of different results of extremum theory can be obtained by using this integrated technique.