Lectures and learning material
Here you can find a tentative overview of the lecture. This plan will be continuously updated. The recordings of the online lectures can be found on blackboard.
Generally, the lecture uses both Tröltzsch's book on optimal control with PDE constraints (you may also use the German version of the same book) and the new book by A. Manzoni, A. Quarteroni, S. Salsa:
- Tr … F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, AMS Graduate Studies in Mathematics, v. 112, 2010.
- MQS … A. Manzoni, A. Quarteroni, S. Salsa, Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications, Springer, 2021. Individual chapters are available at Springer link.
Additional sources we might use:
- 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
- DlR J.C. De los Reyes, Numerical PDE-Constrained Optimization, 2015. Available online via Springer link
If you need some additional background on PDEs, I suggest to have a look at Evans' book or the book by Renardy/Rogers:
- Ev … L.C. Evans, Partial Differential Equations, AMS Graduate Studies in Mathematics, v. 19, 2010.
- RR … M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, Text in Applied Mathematics, Springer, 2005 Springer Link
A nice well-written book treating both theoretical and numerical methods for partial differential equations:
- LT … S. Larsson, V. Thomée, Partial Differential Equations with Numerical Methods, 2003.
Jupyter notebooks
All Jupyter notebooks are uploaded to a public github repository, you can either download individual notebooks from there or just clone (and regularly pull) the entire git repository. Below you'll also find individual links to specific notebooks used in the tutorial sessions.
Lecture plan
| Date | Topics | Notes | Notebooks | Reading material |
|---|---|---|---|---|
| Week 2 | Introduction (AM) Finite-dimensional optimal control (DH) | Chapter_01.pdf optii_lecture2_dh.pdf | Lecture 01: Tr 1.2, MQS 1.1, 1.2 Lecture 02: Tr 1.4 |
|
| Week 3 | Weak solution of elliptic PDEs (AM) Finite element method, Julia and Gridap (AM) | Chapter_03-IntroWeakPDE-NumPDE-LiveNotes.pdf | Notebooks can be found at github | |
| Week 4 | Linear-quadratic elliptic optimal control problems (DH) Existence of optimal controls (DH) | optii_lecture6_dh.pdf optii_lecture7_dh.pdf fa-toolbox.pdf | ||
| Week 5 | Frechet and Gateaux differentiability (DH) First-order optimality conditions (DH) | optii_lecture8_dh.pdf optii_lecture9_dh.pdf | ||
| Week 6 | Box constraints and projection formula (DH, Feb. 9) | optii_lecture10_dh.pdf | ||
| Week 7 | Gradient based descent methods I+II (AM) | optii_numerical_methods.pdf | ||
| Week 8 | Project gradient method (AM) Coding tutorial (AM) | Notebooks can be found at github, in particular have a look at PoissonOCP.ipynb. A solution for the descent algorithm can be found in DescentMethods.jl. | ||
| Week 9 | no lectures | |||
| Week 10 | Error estimates for a semi-discretized OCP, the primal dual active set method | Dietmar's slides with my handwritten notes lecture-ocp-error-estimate-active-set-methods.pdf | ||
| Week 11 | two example problems project presentation addendum to problem formulation | optii_lecture_march_16.pdf opt_ii_project_2023.pdf addendum_new.pdf | ||
| Week 12 | project work, short tutorial on how to formulate and implement state problems with mixed boundary conditions | Notebooks can be found at github, in particular have a look at poisson_multiple_boundary_conditions.ipynb. | ||
| Week 13 | project work | |||
| Week 14 | Easter holidays | |||
| Week 15 | project work and submission | |||
| Week 16 | Introduction to parabolic optimal control (DH) Analysis for parabolic state equations (DH) numerical simulation of parabolic PDEs (AM) | optli_lecture_april_18a.pdf rothe_method_for_parabolic_eqns.pdf | ||
| Week 17 | numerical methods for parabolic optimal control problems (AM) | optii_lecture_num_meth_parabolic_ocp.pdf | MQS: Ch. 8.1 (except p. 269) , 8.2 | |
| Week 18 | real world parabolic control problems (DH) | optii_lecture_may_2.pdf |