Lecture on Optimal Control of Partial Differential Equations

Specialized course within the Optimization Master 2016/17, University Paris-Saclay


The Exam will take place on March 30 at 15h45 in Amphi Sauvy.

The course takes place Thursdays starting on February 2nd, from 15h45 to 18h15 in Amphi Sauvy.


basic knowledge in functional analysis and PDE theory are recommended


The aim of this course is to give an introduction in optimal control of partial differential equations. The theory aims to find control functions that minimizes cost functions under constraints given by partial differential equations and has applications in aeronautics, mechanical engineering, and the life sciences.


The course considers optimal control problems for linear and semilinear elliptic partial differential equations. The main focus lies on existence of optimal controls, distributed and boundary control problems, necessary and sufficient optimality conditions, semismooth Newton methods for problems with constraints on the controls, and discretization concepts based on finite elements.

Lecture notes

Optimal Control of Partial Differential Equations     (version - large font)


Ex1     Pr1

Ex2     Pr2

Ex3     Pr3

Ex4     Pr4

Ex5     Pr5


M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich: Optimization with PDE Constraints, Springer, 2008.

F. Tröltzsch: Optimal Control of Partial Differential Equations - Theory, Methods and Applications. Graduate Studies in Mathematics, Vol. 112. American Mathematical Society, Providence, Rhode Island, 2010.

M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces, MOS-SIAM Series on Optimization, 2011.