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

Report

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.

Authors: Cartis, C; Gould, N; Toint, P

• Publisher: Unspecified
• Publication date: 2008-02-01