Trust−region and other regularisations of linear least−squares problems
Coralia Cartis‚ Nicholas I. M. Gould and Philippe L. Toint
Abstract
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|| ≤ Δ is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b||2q and a regularisation term ||x||2p 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 resulting algorithms are available as part of the GALAHAD optimization library.
Details
| Institution |
Oxford University Computing Laboratory |
| Month |
February |
| Number |
NA−08/02 |
| Year |
2008 |
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