Regularization of Nonlinear Least Squares Problems

  • Guy ChaventEmail author
Part of the Scientific Computation book series (SCIENTCOMP)


We consider in this chapter various approaches for the regularization of the general NLS problem (1.10), recalled here for convenience:
$$\hat{x}\quad \mbox{ minimizes }\quad J(x) = \frac{1} {2}\|\varphi (x) - {z\|}_{F}^{2}\quad \mbox{ over }\quad C. $$
and we suppose throughout the chapter that it satisfies the minimum set of hypothesis (1.12) or (4.2).

We develop three of the five approaches described in Sect. 1.3.4 of the introduction: Levenberg–Marquardt–Tychonov (LMT), state-space, and adapted regularization. The two remaining approaches, regularization by parameterization and regularization by size reduction of the admissible parameter set, have been already addressed in Chaps. 3 and 4, respectively.


Regularization Parameter Regularity Condition Tangent Cone Observation Operator Deflection Condition 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Ceremade, Université Paris-DauphineParis Cedex 16France
  2. 2.Inria-RocquencourtLe Chesnay CedexFrance

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