Mathematics

Optimal Control of Partial Differential Equations

Module code: G5214
Level 6
15 credits in spring teaching
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

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.

Module learning outcomes

  • Explain basic concepts in optimal control of partial differential equations.
  • Show mastery of the existence theory for elliptic optimal control problems.
  • Derive necessary optimality conditions for elliptic optimal control problems.
  • Understand standard numerical methods for their solution.