Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle

The chapter is a survey on recently proposed technique for parameter identification in partial differential equations. This technique combines natural linearization of an identification problem with the Tikhonov scheme, where the regularization parameter is chosen adaptively by means of the so-called balancing principle. We describe the natural linearization approach and show how it can be treated within the framework of Tikhonov regularization as a problem with noisy operator and noisy data. Then the balancing principle is discussed in the context of such a problem. We demonstrate the performance of proposed technique in some typical parameter identification problems.