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Regularization of Nonlinear Least Squares Problems

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

Abstract

We consider in this chapter various approaches for the regularization of the general NLS problem (1.10), recalled here for convenience:
$$\hat{x}\quad \mbox{ minimizes }\quad J(x) = \frac{1} {2}\|\varphi (x) - {z\|}_{F}^{2}\quad \mbox{ over }\quad C. $$
(5.1)
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.

Keywords

Regularization Parameter Regularity Condition Tangent Cone Observation Operator Deflection Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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