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Kaj Madsen - DTU Informatics•Head of Department


Non-linear approximation and engineering design

The Space Mapping principle is an exiting new way to solve problems with very costly function evaluations - trying to find the connection (a "space mapping") between two different models of the same problem: An easy model, and a more accurate, expensive model. More information, and access to a MATLAB toolbox, is available here.

The space mapping work is done in colaboration with Bandler Corporation, Ontario, Canada.

Kaj Madsen - DTU Informatics•Head of Department

Algorithms for Non-linear Approximation are used for finding optimal values for the parameters in a mathematical model of an economic, physical or engineering problem. We have developed algorithms and software for approximation where the objective to be minimized is the deviation measured in one of the following ways:

  • The minimax method where the largest deviation is minimized.
  • The usual least squares method.
  • The L1 method which minimize the sum of the absolute values.
  • The Huber method which is a robust estimator, less robust than L1 and more robust than least squares - depending on a parameter.
A software package is available on request.


The topic of non-linear optimization is tought in the DTU course:
02611: Optimization and Data Fitting (Fall semester)

Teaching demos.


  • NEOS: Network-Enabled Optimization System. Maintained by The Optimization Technology Center which is a joint enterprise of Argonne National Laboratory and Northwestern University, USA. It was founded in 1994 with support from the U.S. Department of Energy and Northwestern University.
  • Some test examples for global optimization, selected by Kaj Madsen.