Lecture plan
Here you can find a tentative overview of the lecture. This plan will be continuously updated. My handwritten notes for the lecture are available on blackboard.
 Tr … F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, AMS Graduate Studies in Mathematics, v. 112, 2010.
 HPUU … M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE Constraints, Mathematical Modelling: Theory and Applications, v. 23, Springer, 2009.
 Available online via Springer link
 IK … K. Ito, K. Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications, Advances in Design and Control, SIAM, 2008.
 CNQ … X. Chen, Z. Nashed, L. Qi … Smoothing methods and semismooth methods for nondifferentiable operator equations, SIAM Numer. Anal. 38(4), pp. 12001216, 2000.
 Ev … L.C. Evans, Partial Differential Equations, AMS Graduate Studies in Mathematics, v. 19, 2010.
 SGGHL … O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen, Variational Methods in Imaging, Applied Mathematical Sciences, v. 167, Springer 2009.
 Available online via Springer link
 EHN … H. W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems, Mathematics and Its Applications, v. 375, Kluwer Academic Publishers, 1996.
Date  Topics  Slides  Reading material / References 

Week 2  Introduction Lebesgue measure Lebesgue integration  Introduction  Ev App E Ev App E 
Week 3  \(L^p\)spaces Integral functionals on \(L^p\) Weak topology and weak convergence  Tr 2.2  
Week 4  Existence of minimisers of integral functionals on \(L^p\) Sobolev spaces Calculus of variations  Tr 2.2, Ev 5.2 Ev 8.1, 8.2 

Week 5  Euler–Lagrange equations Differentiation in Banach spaces Precise derivation of Euler–Lagrange equations  Ev 8.1 Tr, 2.6 Ev 8.2 

Week 6  Galerkin methods Lavrentiev phenomenon Weak formulation of PDEs Lax–Milgram Theorem Browder–Minty theory  Tr 2.3 Tr 2.4, Ev 6.2 Tr 4.2 

Week 7  Existence and stability for monotone, quasilinear PDEs Introduction to optimal control problems Existence of optimal controls Review of finite dimensional constrained optimisation  Tr 4.2 Tr 4.4 Tr 1.4 

Week 8  Presentation of projects Optimality system for elliptic problems Reduced functional and gradient Adjoint equation Lagrangian formulation  Tr 2.8, 2.10 Tr 2.8 Tr 2.8 Tr 2.10 

Week 9  Parabolic control problems Problems with control constraints Gradient projection method  Tr, Ch. 3.4, 3.5 Tr, Ch. 2.8 Tr, Ch. 2.12 

Week 10  Optimal control with nonlinear PDEs Fréchet differentiability of superposition operators Newton's method in Banach spaces Newton's method and SQP for optimal control  Tr 4.6 Tr 4.3 Tr 4.11 

Week 11  Higher order differentiability conditions Active set methods Semismooth Newton methods Relation between active set and semismooth Newton methods  Tr 4.3 Tr 4.11 CNQ IK 8.4 

Week 12  Quarantine  
Week 13  Inverse problems Parameter identification problems for PDEs Illposed problems and regularisation Tikhonov regularisation Reconstruction errors  SGGHL 3.1, EHN 3.1, 5.1  
Week 14  Parameter choice methods Discrepancy principle Lcurve Quasioptimality Iterative regularisation Landweber method  EHN 4.3, 4.5 EHN 6.1 

Week 16  Student presentations  
Week 17  Summary  Summary 