Nonlinear inverse problems are solved in many applications such as geophysics and medical physics. In many cases these problems can be represented as a distributed parameter estimation problems.

In this talk we explore methods for the solution of such problems. We will show that the Newton step is only s lightly more expensive than the Gauss-Newton step and utilize quasi-Newton techniques in order to obtain a cheap approximation to the Newton step.

We demonstrate the ideas on a large 3D inverse problem of estimating the conductivity when the underline equations are Maxwell's equations.

MINISIMPOSIUM SESSION: 1. Optimization problems in differential equations