Why Curvature in L-Curve: Combining Soft Constraints

  • Uram Anibal Sosa AguirreEmail author
  • Martine Ceberio
  • Vladik Kreinovich
Part of the Studies in Computational Intelligence book series (SCI, volume 539)


In solving inverse problems, one of the successful methods of determining the appropriate value of the regularization parameter is the L-curve method of combining the corresponding soft constraints, when we plot the curve describing the dependence of the logarithm x of the mean square difference on the logarithm y of the mean square non-smoothness, and select a point on this curve at which the curvature is the largest. This method is empirically successful, but from the theoretical viewpoint, it is not clear why we should use curvature and not some other criterion. In this paper, we show that reasonable scale-invariance requirements lead to curvature and its generalizations.


soft constraints inverse problems regularization L-curve curvature 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Uram Anibal Sosa Aguirre
    • 1
    Email author
  • Martine Ceberio
    • 1
  • Vladik Kreinovich
    • 1
  1. 1.Computational Sciences Program and Department of Computer ScienceUniversity of TexasEl PasoUSA

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