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OnderzoekBernoulli InstituteCalendarColloquia - Mathematics

Colloquium Mathematics/ Dr. T. van Leeuwen

When:Tu 16-10-2018 16:00 - 17:00
Where:5161.0293 (Zernike, Bernoulliborg)


Constraint-relaxation for PDE-constrained optimization in inverse problems


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