Abstract
Nonlinear least squares problems are extremely important in many domains of mathematical programming applications, e.g. maximum likelihood estimations, nonlinear data fitting or parameter estimation, respectively. A large number of special purpose algorithms is available in the unconstrained case, but only very few methods were developed for the nonlinearly constrained case. The paper shows that a simple transformation of the original problem and its subsequent solution by a general purpose sequential quadratic programming algorithm retains typical features of special purpose methods, i.e. a combination of a Gauß-Newton and a quasi-Newton search direction. Moreover the numerical investigations indicate that the algorithm can be implemented very easily if a suitable sequential quadratic programming code is available, and that the numerical test results are comparable to that of special purpose programs.
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© 1988 Birkhaürser Verlag Basel
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Schittkowski, K. (1988). Solving Constrained Nonlinear Least Squares Problems by a General Purpose SQP-Method. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_19
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DOI: https://doi.org/10.1007/978-3-0348-9297-1_19
Publisher Name: Birkhäuser Basel
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