Location: MIC-Arena, Maria-Goeppert-Str. 3, 23562 Lübeck
Title: Numerical Optimization with Hyperbolic PDE-Constraints
Abstract: Optimization problems with first-order hyperbolic Partial Differential Equations (PDEs) as constraints arise in numerous applications and have a long and rich mathematical history. Hyperbolic PDEs are characterized by a velocity field and initial conditions. In many applications, one or both of these quantities are unknown and need to be estimated or can be modified to optimize an objective function. Some examples are the Monge-Kantorovich problem of optimal mass transport, motion detection using optical flow, image registration, and fluid flow estimation in geophysical explorations.
In this talk, I will discuss numerical strategies for numerically solving optimization problems with hyperbolic PDE-constraints. I will focus on applications in image registration and follow a discretize-then-optimize strategy. This leads to a large-scale constrained nonlinear optimization problem.
The main focus is on handling the constraints, which is challenging, for example, due to restrictions of time step size to remain numerical stability. I will discuss some existing and some recent strategies and compare them using numerical examples.
The talk will be given in German or English depending on the audience.
