Trust-region and other regularisations of linear least-squares problems

@inproceedings{Cartis2008TrustregionAO,
  title={Trust-region and other regularisations of linear least-squares problems},
  author={Coralia Cartis and Nicholas I. M. Gould and Philippe L. Toint},
  year={2008}
}
We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ‖x‖ ≤ ∆ is imposed on the size of the solution, and in which the least value of linear combinations of ‖Ax−b‖q2 and a regularisation term ‖x‖ p 2 for various p and q = 1, 2 is sought. In each case, one of more “secular” equations are derived, and fast Newton-like solution procedures are suggested. The… CONTINUE READING
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