This module provides an introduction to optimal control problems for partial differential equations. Starting from basic concepts in finite dimensions (existence, optimality conditions, adjoint, Lagrange functional, KKT system), we will study the theory of linear-quadratic elliptic optimal control problems (weak solutions, existence of optimal controls, adjoint operators, necessary optimality conditions, Lagrange functional, adjoint as Lagrangian multiplier) as well as basic numerical methods for their solution (gradient method, projected gradient method, active set strategy).

By the end of the module, you should be able to

• explain basic concepts in optimal control of PDE,
• show mastery of the existence theory for elliptic optimal control problems,
• derive necessary optimality conditions for elliptic optimal control problems,
• understand basic numerical methods for their solution.

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TCC = Taught Course CentreLink opens in a new window, which is an online series of PhD lecture modules organised by Oxford, Warwick, Imperial, Bristol, Bath and Swansea.

Lecturer: Prof Bertram Düring

Lectures: TCC Optimal Control of Partial Differential Equations will run 10:00-12:00 on Wednesdays from 22 January 2025 to 12 March 2025. It will run in hybrid form, on Teams and in B0.06 in Zeeman Building, University of Warwick.

Registration: For the Teams link, please register with tcc@maths.ox.ac.uk, specifying your email address for Teams access.

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