Regularization using a parameterized trust region subproblem

  • Authors:

  • Oleg Grodzevich;Henry Wolkowicz

  • Affiliations:

  • University of Waterloo, Department of Management Sciences, N2L 3G1, Waterloo, ON, Canada;University of Waterloo, Department of Combinatorics and Optimization, N2L 3G1, Waterloo, ON, Canada

  • Venue:
  • Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
  • Year:
  • 2008

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Abstract

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.