Optimal Control of Partial Differential Equations (G5214)

15 credits, Level 6

Spring teaching

You will be introduced to optimal control problems for partial differential equations. Starting from basic concepts in finite dimensions (existence, optimality conditions, adjoint, Lagrange functional and KKT system) you will study the theory of linear-quadratic elliptic optimal control problems (weak solutions, existence of optimal controls, adjoint operators, necessary optimality conditions, Langrange functional and adjoint as Langrangian multiplier) as well as basic numerical methods for your solution (gradient method, projected gradient method and active set strategy). The extension to semi-linear elliptic control problems will also be considered.


100%: Lecture


20%: Coursework (Problem Set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 36 hours of contact time and 114 hours of independent study.

This module is running in the academic year 2017/18. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.


This module is offered on the following courses: