Information about the lecture

here

Linear and non-linear partial differential equations (PDEs) constitute one of the most widely used mathematical frameworks for modelling various physical or technological processes, such as fluid flow, structural deformations, propagation of acoustic and electromagnetic waves amongst countless other examples. Improvement in such processes therefore requires modelling and solving optimization problems constrained with PDEs, and more generally convex and non-convex optimization problems in spaces of functions.

In this course you will learn the theory pertinent for analysing optimization problems of this type and also fundamental numerical methods for solving these problems. We will mostly concentrate on the optimal control of processes governed with linear and semilinear elliptic PDEs.

We will aim at a reasonably self-contained course but of course some knowledge of PDEs, functional analysis, and optimization theory is beneficial.

The lecture is held by Markus Grasmair, room 1040 SB2, markus.grasmair@math.ntnu.no, jointly with Dietmar Hömberg, hoemberg [at] wias [dash] berlin [dot] de.

• Tuesday 14:15-16:00, seminar room 734.
• Friday 15:15-17:00, seminar room 734.

The first lecture will be held on Friday, January 12.

• From January 24 - February 7, there will be additional lectures on Wednesdays, 09:15-11:00, in seminar room 656.

The exercises will be published here.

When and where: TBD

The textbook is De los Reyes.

• J.C. De los Reyes, Numerical PDE-Constrained Optimization, 2015. Available online via Springer link
• F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, AMS Graduate Studies in Mathematics, v. 112, 2010. Amazon AMS
• 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
• Eds.: Lorenz T. Biegler, M. Heinkenschloss, O. Ghattas, B. van Bloemen Waanders, Large-Scale PDE-Constrained Optimization, 2003. Available online via Springer link
• Eds.: L.T. Biegler , O. Ghattas , M. Heinkenschloss , D. Keyes and B. van Bloemen Waanders, Real-Time PDE-Constrained Optimization, 2007. Available online via SIAM
• L.C. Evans, Partial Differential Equations, AMS Graduate Studies in Mathematics, v. 19, 2010. Amazon AMS

There will be an oral exam at the end of the course.