Lecture on Optimal Control of Partial Differential Equations

Specialized course within the Optimization Master 2017/18, University Paris-Saclay


Additional exercise class: March 20, time: 1:15pm-2:30pm, room: Amphi Curie


Tuesdays,   9am - 12:20, amphitheatre Painlevé, Ecole polytechnique

Jan 30; Feb 6, 13, 20; March 6, 20

Exam: March 27, start: 9am, amphi Painlevé


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


FEniCS Paraview


Ex1   P1

Ex2   P2

Ex3   P3

Ex4   P4-1   P4-2

Ex5   FEniCS-code

Ex6   P6


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.