Colloquium Mathematics/ Dr. T. van Leeuwen

Title:

Constraint-relaxation for PDE-constrained optimization in inverse problems

Abstract:

In many applications, such as exploration geophysics, seismology and ultrasound imaging, we want to estimate material properties from indirect observations. We can pose the inverse problem as a non-linear data-fitting problem: fit the coefficients of a partial differential equation (PDE) such that its solution fits the observations approximately.  The strict constraint given by the PDE typically results in a very non-linear optimization problem. Although black-box optimization methods can be applied in straightforward fashion, convergence is heavily dependent on the initial guess.

By relaxing the constraints we mitigate some of this non-linearity and gain the freedom to incorporate model-errors at the same time. However, solving the resulting optimization problem numerically deserves special attention since we can no longer use black-box PDE solvers. In this talk I will discuss several aspects of this relaxation and present numerical results to illustrate some of the issues.

Colloquium coordinators are Prof.dr. A.J. van der