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The convergence of the damped Levenberg-Morrison-Marquardt- resp. Gauss- Newton-method in adequate nonlinear regression. (English) Zbl 0574.65149
For adequate nonlinear least-squares problems P. Deuflhard and V. Apostolescu [Functional analysis, numerical analysis and optimization, Spec. Top. appl. Math., Proc. Semin. GMD, Bonn 1979, 129- 150 (1980; Zbl 0443.65049)] have proposed a relaxation strategy for the damped Gauss-Newton-method, yet they couldn’t show its convergence in case of (modified) ”natural scaling”. Subsequently, such a ”globalized” convergence result will be derived for a subclass of adequate regression models; yet, to ensure the theoretical ”damping property” with exact natural scaling, one has to introduce a kind of ”Levenberg-Morrison- Marquardt”-damping occasionnally.

65C99 Probabilistic methods, stochastic differential equations
65K05 Numerical mathematical programming methods
62J02 General nonlinear regression