PDE-Constrained Optimization

Summer Course on PDE-Constrained Optimization

July 27, 2013

Michael Ulbrich (Tech. Univ. Munich, Germany) 

Christian Meyer (Tech. Univ. Dortmund, Germany)

09:00-09:50 Registration
09:50-10:00 Opening Remarks 1
10:00-13:00 School Lectures (30 min. break included)
13:00-14:30 Lunch
14:30-17:30 School Lectures (30 min. break included)
19:00-22:00 Summer School Dinner


Models of complex processes in natural sciences, engineering, and economics often canonically result in systems of partial differential equations (PDEs). Although simulation already provides valuable insights, the efficient optimization and control of the underlying system opens up a whole new dimension of fascinating possibilities. Exploring this high potential poses many challenges in both the analysis and numerical solution of PDE-constrained optimization problems. Achieving tractable approaches requires a unique interplay between the theory and methods of mathematical optimization, partial differential equations, numerical analysis, and scientific computing. 

This summer school provides an introduction to the field of PDE-constrained optimization. The presentation follows an accessible, unifying functional analytic framework to develop the main concepts, and illustrates them by suitable model problems. Existence of solutions, optimality conditions, and efficient optimization methods will be discussed, along with some introductory material on PDEs and FE discretization. The course concludes with ongoing and future research directions and with several examples of more advanced applications.