Regularization Using a Parameterized Trust Region Subproblem

  • Oleg Grodzevich
  • Henry Wolkowicz
    • Categories Applications - Science and Engineering, Biomedical Applications, Nonlinear Systems and Least-Squares Tags , , , , Short URL: https://optimization-online.org/?p=9751

    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 {\em trust-region subproblem}, \TRS, approach that makes use of the {\em L-curve} maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We use derivative information, and properties of an algorithm for solving the TRS, to efficiently move along points on the L-curve and reach the point of maximum curvature. We do not find a complete characterization of the L-curve. A MATLAB code for the algorithm is tested and a comparison to the conjugate gradient least squares, CGLS, approach is given and analyzed.

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    Research Report CORR 2005-11 University of Waterloo, Waterloo, Canada

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