## Optimization and Systems Theory Seminar

Department of Mathematics, KTH

### Jerry Eriksson

Department of Computing Science,

Umeå University,

S-901 87 Umeå,

Sweden.

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 Umeå 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.

Calendar of Seminars

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