Trust-region and other regularisations of linear least-squares problems
C. Cartis, N. I. M. Gould and Ph. L. Toint
Report 08/04 February 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|| <= Delta is imposed
on the size of the solution, and in which the least value of linear
combinations of ||Ax-b||_2^q and a regularisation term ||x||_2^p 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.