Mathematical Programming

, Volume 116, Issue 1, pp 193–220

Regularization using a parameterized trust region subproblem


DOI: 10.1007/s10107-007-0126-4

Cite this article as:
Grodzevich, O. & Wolkowicz, H. Math. Program. (2009) 116: 193. doi:10.1007/s10107-007-0126-4


We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional trust-region subproblem, TRS, approach that makes use of the L-curve maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We apply a parameterized trust region approach to estimate the region of maximum curvature of the L-curve and find the regularized solution. This exploits the close connections between various parameters used to solve TRS. A MATLAB code for the algorithm is tested and a comparison to the conjugate gradient least squares, CGLS, approach is given and analysed.


RegularizationTrust region subproblemIll-conditioned problemsL-curveImage restoration

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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Management SciencesUniversity of WaterlooWaterlooCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada