On solving trust-region and other regularised subproblems in optimization (2010)

First Author: Gould N

Attributed to:  Algorithms for Large-Scale Nonlinearly Constrained Optimization funded by EPSRC


The solution of trust-region and regularisation subproblems that arise in unconstrained optimization is considered. Building on the pioneering work of Gay, Moré and Sorensen, methods that 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 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. © Springer and Mathematical Programming Society 2009.

Bibliographic Information

Digital Object Identifier: http://dx.doi.org/10.1007/s12532-010-0011-7

Publication URI: http://dx.doi.org/10.1007/s12532-010-0011-7

Type: Journal Article/Review

Volume: 2

Parent Publication: Mathematical Programming Computation

Issue: 1