The Mathematical Institute, University of Oxford, Eprints Archive

On solving trust-region and other regularised subproblems in optimization

Dollar, H. Sue and Gould, Nicholas I. M. and Robinson, Daniel P. (2009) On solving trust-region and other regularised subproblems in optimization. Technical Report. Mathematical Programming (Springer). (Submitted)

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Abstract

The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, Mor´e and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both globally and asymptotically at least superlinearly convergent in all cases, including in the notorious hard case. Numerical experiments validate the effectiveness of our approach. The resulting software is available as packages TRS and RQS as part of the GALAHAD optimization library, and is especially designed for large-scale problems.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Operations research, mathematical programming
A - C > Calculus of variations and optimal control
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:868
Deposited By:Lotti Ekert
Deposited On:17 Dec 2009 08:08
Last Modified:17 Dec 2009 08:08

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