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- Ingrid Bongartz, Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
- ACM Trans. Math. Softw.
- 1995

The purpose of this article is to discuss the scope and functionality of a versatile environment for testing small- and large-scale nonlinear optimization algorithms. Although many of theseâ€¦ (More)

- Nicholas I. M. Gould, Dominique Orban, Philippe L. Toint
- ACM Trans. Math. Softw.
- 2003

The initial release of CUTE, a widely used testing environment for optimization software, was described by Bongartz, et al. [1995]. A new version, now known as CUTEr, is presented. Features includeâ€¦ (More)

- Carsten Keller, Nicholas I. M. Gould, Andrew J. Wathen
- SIAM J. Matrix Analysis Applications
- 2000

The problem of nding good preconditioners for the numerical solution of in-deenite linear systems is considered. Special emphasis is put on preconditioners that have a 2 2 block structure and whichâ€¦ (More)

- Nicholas I. M. Gould, Mary E. Hribar, Jorge Nocedal
- SIAM J. Scientific Computing
- 2001

We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization Our approach is based implicitly on aâ€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- Math. Program.
- 2011

An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981,â€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- Math. Program.
- 2011

An Adaptive Regularisation framework using Cubics (ARC) was proposed for unconstrained optimization and analysed in Cartis, Gould & Toint (Part I, 2007). In this companion paper, we further theâ€¦ (More)

- Nicholas I. M. Gould, Jennifer A. Scott
- SIAM J. Scientific Computing
- 1998

We investigate the use of sparse approximate-inverse preconditioners for the iterative solution of unsymmetric linear systems of equations. We consider the approximations proposed by Cosgrove, Diaz,â€¦ (More)

- Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
- Math. Program.
- 1991

Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paperâ€¦ (More)

- Nicholas I. M. Gould, Stefano Lucidi, Massimo Roma, Philippe L. Toint
- SIAM Journal on Optimization
- 1999

The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, theâ€¦ (More)

- Roger Fletcher, Nicholas I. M. Gould, Sven Leyffer, Philippe L. Toint, Andreas WÃ¤chter
- SIAM Journal on Optimization
- 2002

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239â€“269] that decomposes the step into its normal and tangential components allowsâ€¦ (More)