Optimization and Systems Theory Seminar
Department of Mathematics, KTH

Jerry Eriksson
Department of Computing Science,
Umeň University,
S-901 87 Umeň,
E-mail: Jerry.Eriksson@cs.umu.se
Homepage: http://www.cs.umu.se/~jerry/

Regularization-A smoothing technique for all nonlinear least squares problems?

The natural method for solving nonlinear least squares (NLS) problems is the classical Gauss-Newton (GN) method. By using only first derivative information (Jacobian, J) fast convergence is often achieved. However, it is well-known that the pure GN method breaks down if J is rank-deficient or ill-conditioned. Existing techniques try to stabilize locally where the difficulties occur. Our approach is to regularize the original problem, i.e., solve a well-conditioned problem that are close to the original problem. This smoothing technique enables us to solve problems that are rank-deficient or ill-conditioned everywhere in the solution space. In this talk, basic ideas and theory of truncated SVD and Tikhonov regularization will be discussed. The optimization group in Umeň currently works extensively with Tikhonov regularization of NLS0 and examples of applications will be given in parameter identification problems such as signal processing, ODE, PDE, and neural network training.

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Last update: September 30, 1996 by Anders Forsgren, andersf@math.kth.se.