Nick Gould

Senior Fellow

Continuous Optimisation

Before starting university in Oxford, I worked for 8 months in the Department of Numerical Analysis and Computing at the National Physical Laboratory in Teddington. I finished my D.Phil. at Oxford in 1982, having spent one year in the O.R. Department at Stanford University in California. I then spent three years as an Assistant Professor in the Department of Combinatorics and Optimization at the University of Waterloo, Ontario, Canada, before returning to England and joining the Numerical Analysis Group in the Computer Science and Systems Division at AEA Harwell.

I moved with the Group to the Central Computing Department (as it was then) at RAL in 1990 and have been there almost ever since. I spent a sabbatical year at CERFACS in Toulouse, France, during 1993.

LANCELOT book Complexity book Trust-region book I am a visiting Professor within the Department of Mathematics and Statistics at the University of Edinburgh, and at the University of Oxford. I won the Leslie Fox prize in numerical analysis in September 1986, and the Beale-Orchard-Hays prize for excellence in computational mathematical programming in August 1994. In May 2009, I was elected as one of 183 inaugural SIAM Fellows. I have published three books: the first on the software package LANCELOT in 1992, the second on trust-region methods in 2000, and the most recent on evaluation complexity of algorithms for nonconvex optimization in 2022. I was editor-in-chief of the SIAM Journal on Optimization from 2005 until 2010, and an associate editor for the ACM Transactions on Mathematical Software, for the IMA Journal of Numerical Analysis, for Mathematics of Computation, and for Mathematical Programming, and as well as being an Area Editor for Mathematical Programming Computation, until 2016.

Carling Cup 2008 My research interests are currently on the theory and practice of optimization methods, on numerical linear algebra, on large-scale scientific computation, and on the links between these fields. My other interests include church-bell ringing, hill walking, messing about on canals, mushroom collecting, and brewing and appreciating cask-conditioned ales of all varieties. I am a long-suffering supporter of Tottenham Hotspur FC.

In 2006, I was appointed as Professor of Numerical Optimisation and Tutorial Fellow of Exeter College at the University of Oxford. I returned full-time to RAL in 2008. I became an STFC Senior Fellow in 2011, and have worked half time since the summer of 2017.

My CV (PDF) gives all the gory details.

  • Numerical optimization
  • Numerical analysis
  • Linear algebra
  • Large scale scientific computation
  • High performance computation

ORCID id: 0000-0002-1031-1588, Web of Science Reseacher id: AAS-2273-2020

Books:

  1. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Evaluation complexity of algorithms for nonconvex optimization: theory, computation and perspectives'', MOS-SIAM Series on Optimization, SIAM, Philadelphia (2022), ISBN 978-1-611976-98-4.

  2. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Trust-region methods'', SIAM/MPS Series on Optimization, SIAM, Philadelphia (2000), ISBN 0-89871-460-5.

  3. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``LANCELOT: a Fortran package for large-scale nonlinear optimization, release A'', Series in Computational Mathematics 17, Springer-Verlag, Berlin (1992), ISBN 3-540-55470-X.

Edited collections:

  1. N. I. M. Gould, S. Leyffer and Ph. L. Toint, ``Nonlinear programming: theory and practice'' Mathematical Programming B 100:1 (2004).

  2. I. S. Duff, N. I. M. Gould, C. C. Douglas and L. Giraud, ``Direct methods, linear algebra in optimization, and iterative methods: Proceedings from the International Linear Algebra Year workshops, September 1995-June 1996'' BIT 37:3 (1997).

  3. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Large-Scale Optimization--Applications'' Mathematical Programming B 48:1 (1990).

  4. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Large-Scale Optimization'' Mathematical Programming B 45:3 (1989).

Refereed articles:

    1. J. Fowkes, N. I. M. Gould and J. A. Scott, ``Approximating sparse Hessian matrices using large-scale linear least squares''. Numerical Algorithms. (2023) DOI:s11075-023-01681-z. (PDF)

    2. J. Fowkes and N. I. M. Gould, ``GALAHAD 4.0: an open source library of Fortran packages with C and Matlab interfaces for continuous optimization''. Journal of Open Source Software. 8(87) (2023) 4882. (PDF)

    3. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints''. SIAM Journal on Optimization. 30(1) (2020) 513–541. (PDF)

    4. C. Cartis, N. I. M. Gould and M. Lange, ``On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces''. BIT 60(2) (2020) 583-589. (PDF)

    5. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``A concise second-order complexity analysis for unconstrained optimization using high-order regularized models''. Optimization Methods and Software 35(2) (2020) 243-256. (PDF)

    6. N. I. M. Gould and V. Simoncini, ``Error estimates for iterative algorithms for minimizing regularized quadratic subproblems''. Optimization Methods and Software 35(2) (2020) 304-328. (PDF)

    7. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization''. Proceedings of the International Congress of Mathematics, Rio de Janeiro, 2018, Volume 3 (2019) 3697-3737. (PDF)

    8. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled {KKT} conditions and high-order models''. In ``Approximation and Optimization'' (I. C. Demetriou and P. M. Pardalos, eds.), Springer Optimization and Its Applications 145 (2019) 5-26. (PDF)

    9. N. I. M. Gould, T. Rees and J. A. Scott, ``Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems''. Computational Optimization and Applications 73(1) (2019) 1-35. (PDF)

    10. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Universal regularization methods-varying the power, the smoothness and the accuracy''. SIAM Journal on Optimization. (2018). 29(1) (2019) 595–615. (PDF)

    11. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Optimality of orders one to three and beyond : characterization and evaluation complexity in constrained nonconvex optimization''. Journal of Complexity 53 (2019) 68-94. (PDF)

    12. F. Furini, E. Traversi, P. Belotti, A. Frangioni, A. Gleixner, N. I. M. Gould, L. Liberti, A. Lodi, R. Misener, H. Mittelmann, N. V. Sahinidis, S. Vigerske and A. Wiegele, ``QPLIB: A Library of Quadratic Programming Instances''. Mathematical Programming Computation 10(2) (2019) 237-265. (PDF)

    13. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Second-order optimality and beyond: characterization and evaluation complexity in nonconvex convexly-constrained optimization''. Foundations of Computational Mathematics 18(5) (2018) 1073–1107. (2018). (PDF)

    14. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients''. Optimization Methods and Software 32(6) (2017) 1273--1298. (PDF)

    15. N. I. M. Gould and D. P. Robinson, ``A dual gradient-projection method for large-scale strictly convex quadratic problems''. Computational Optimization and Applications 67(1) (2017) 1-38. (PDF)

    16. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization''. Mathematical Programming. 161(1-2) (2017) 611-626. (PDF)

    17. F. E. Curtis, N. I. M. Gould, D. P. Robinson and Ph. L. Toint, ``An interior-point trust-funnel algorithm for nonlinear optimization''. Mathematical Programming 161(1-2) (2017) 73-134. (PDF)

    18. N. I. M. Gould and J. A. Scott, ``The state-of-the-art of preconditioners for sparse linear least-squares problems'', ACM Transactions on Mathematical Software 43(4) (2016) Article 36. (PDF)

    19. N. I. M. Gould and J. A. Scott, ``A note on performance profiles for benchmarking software'', ACM Transactions on Mathematical Software 43(2) (2016) Article 15. (PDF)

    20. D. Packwood, J. R. Kermode, L. Mones, N. Bernstein, J. Woolley, N. I. M. Gould, C. Ortner and G. Csány, ``A universal preconditioner for simulating condensed phase materials'', Journal of Chemical Physics. 144(16) (2016) 164109, DOI: 10.1063/1.4947024. (PDF)

    21. N. I. M. Gould, C. Ortner and D. Packwood, ``An efficient dimer method with preconditioning and linesearch''. Mathematics of Computation 85 (2016) 2939-2966. (PDF)

    22. F. E. Curtis, N. I. M. Gould, H. Jiang and D. P. Robinson ``Adaptive augmented Lagrangian methods: algorithms and practical numerical experience''. Optimization Methods and Software 31(1) (2016) 157-186. (PDF)

    23. N. I. M. Gould, Y. Loh and D. P. Robinson ``A nonmonotone filter SQP method : local convergence and numerical results''. SIAM Journal on Optimization. 25:3 (2015) 1885-1911. (PDF) plus full numerical results (PDF)

    24. N. I. M. Gould, D. Orban and Ph. L. Toint, ``An interior-point l1-penalty method for nonlinear optimization''. In ``Recent Developments in Numerical Analysis and Optimization'' (M. Al-Baali, ed), Springer Proceedings in Mathematics and Statistics (2015) 117-150. (PDF)

    25. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods''. SIAM Journal on Numerical Analysis 52(3) (2015) 836-851. (PDF)

    26. N. I. M. Gould, D. Orban and Ph. L. Toint, ``CUTEst : a constrained testing environment with safe threads for mathematical optimization''. Computational Optimization and Applications 60(3) (2015) 545-557. (PDF)

    27. N. I. M. Gould, D. Orban and T. Rees. ``Projected Krylov methods for saddle-point systems''. SIAM Journal on Matrix Analysis and Application 35:4 (2014) 1329–1343. (PDF)

    28. C. Cartis, J. M. Fowkes and N. I. M. Gould ``Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties''. Journal of Global Optimization (2014) DOI: 10.1007/s10898-014-0199-6 (2014) 29 pages. (PDF)

    29. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the complexity of finding first-order critical points in constrained nonlinear optimization''. Mathematical Programming 144(1-2) (2014) 93-106.. (PDF)

    30. N. I. M. Gould, Y. Loh and D. D. Robinson ``A filter method with unified step computation for nonlinear optimization''. SIAM Journal on Optimization. 24:1 (2014) 175–209. (PDF)

    31. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization''. SIAM Journal on Optimization 23(3) (2013) 1553-1574. (PDF)

    32. N. I. M. Gould, D. Orban and D. P. Robinson, ``Trajectory-following methods for large-scale degenerate convex quadratic programming''. Mathematical Programming Computation 5(2) (2013) 113-142, plus 14 page on-line appendices. (PDF) (PDF)

    33. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function''. Optimization Methods and Software 28(3) (2013) 451-457. (PDF)

    34. J. M. Fowkes, N. I. M. Gould and C. L. Farmer, ``A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions''. Journal of Global Optimization 56(4) (2013) 1791-1815. (PDF)

    35. P. A. Browne, C. J. Budd, N. I. M. Gould, H. A. Kim and J. A. Scott, ``A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints''. International Journal for Numerical Methods in Engineering DOI: 10.1002/nme.4367, 18 pages (2012). (PDF)

    36. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``How much patience do you have? A worst-case perspective on smooth nonconvex optimization''. Optima 88 (2012) 1-10. (PDF)

    37. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization''. SIAM Journal on Optimization 22(1) (2012) 66-86. (PDF)

    38. N. I. M. Gould, M. Porcelli and Ph. L. Toint, ``Updating the regularization parameter in the adaptive cubic regularization algorithm''. Computational Optimization and Applications 53(1) (2012) 1-22. (PDF)

    39. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity''. IMA Journal of Numerical Analysis 32(4) (2012) 1662-1695. (PDF)

    40. C. Cartis, N. I. M. Gould and Ph. L. Toint ``Evaluation complexity of adaptive cubic regularization methods for convex unconstrianed optimization''. Optimization Methods and Software DOI: 10.1080/10556788.2011.602076, 23 pages (2011). (PDF)

    41. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Complexity bounds for second-order optimality in unconstrained optimization''. Journal of Complexity 28(1) (2012) 93-108. (PDF)

    42. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming''. SIAM Journal on Optimization 21(4) (2011) 1721-1739. (PDF)

    43. N. I. M. Gould, ``How good are extrapolated bi-projection methods for linear feasibility problems?''. Computational Optimization and Applications 51(3) (2012) 1089-1095 + online appendix. (PDF) (PDF)

    44. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function and derivative-evaluation complexity'' Mathematical Programming 130(2) (2011) 295-319. (PDF)

    45. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results'' Mathematical Programming 127(2) (2011) 156-196. (PDF)

    46. N. I. M. Gould and D. P. Robinson, ``A second-derivative trust-region SQP method with a ``trust-region-free'' predictor step''. IMA Journal of Numerical Analysis 32(2) (2012) 580-601. (PDF)

    47. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the complexity of steepest descent, Newton's method and regularized Newton's methods for nonconvex unconstrained optimization problems''. SIAM Journal on Optimization 20(6) (2010) 2833-2852. (PDF)

    48. N. I. M. Gould, D. P. Robinson and H. S. Thorne, ``On solving trust-region and other regularised subproblems in optimization''. Mathematical Programming Computation 2(1) (2010) 21-57. (PDF); earlier technical report RAL TR-2009-03 with more details.

    49. N. I. M. Gould and D. P. Robinson, ``A second derivative SQP method: local convergence and practical issues''. SIAM Journal on Optimization 20(4) (2010) 2049-2079. (PDF)

    50. N. I. M. Gould and D. P. Robinson, ``A second derivative SQP method: global convergence''. SIAM Journal on Optimization 20(4) (2010) 2023-2048. (PDF)

    51. S. Bellavia, C. Cartis, N. I. M. Gould, B. Morini and Ph. L. Toint, ``Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares''. SIAM Journal on Numerical Analysis 48(1) (2010) 1-29. (PDF)

    52. H. S. Dollar, N. I. M. Gould, M. Stoll and A. J. Wathen, ``Preconditioning Saddle-Point Systems with Applications in Optimization''. SIAM Journal on Scientific Computing 32(1) (2010) 249-270. (PDF)

    53. N. I. M. Gould and Ph. L. Toint, ``Nonlinear programming without a penalty function or a filter.'' Mathematical Programming 122(1) (2010) 155-196 and 131(1-2) (2011) 403-404. (PDF), (PDF)

    54. N. I. M. Gould and V. Simoncini, ``Spectral analysis of saddle point matrices with indefinite leading blocks''. SIAM Journal on Matrix Analysis and Applications 31(3) (2009) 1152-1171. (PDF)

    55. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Trust-region and other regularisations of linear least-squares problems''. BIT 49(1) (2009) 21-53. (PDF)

    56. N. I. M. Gould, ``How good are projection methods for convex feasibility problems?''. Computational Optimization and Applications 40(1) (2008) 1-12. (PDF) (PDF)

    57. H. S. Dollar, N. I. M. Gould, W. H. A. Schilders and A. J. Wathen, ``Using constraint preconditioners with regularized saddle-point problems''. Computational Optimization and Applications 36(2-3) (2007) 249-270. (PDF)

    58. N. I. M. Gould, Y. Hu and J. A. Scott, ``A numerical evaluation of sparse direct solvers for the solution of large, sparse, symmetric linear systems of equations''. ACM Transactions on Mathematical Software 33 (2007) paper 2. (PDF)

    59. N. I. M. Gould and Ph. L. Toint, ``FILTRANE, a fortran 95 filter-trust-region package for solving nonlinear feasibility problems''. ACM Transactions on Mathematical Software 33 (2007) paper 1. (PDF)

    60. H. S. Dollar, N. I. M. Gould, W. H. A. Schilders and A. J. Wathen, ``Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems''. SIAM Journal on Matrix Analysis and Applications 28 (2006) 170-189. (PDF)

    61. H. S. Dollar, N. I. M. Gould and A. J. Wathen, ``On implicit-factorization constraint preconditioners''. in Large Scale Nonlinear Optimization (G. Di Pillo and M. Roma, eds.) Springer Series on Nonconvex Optimization and Its Applications, Vol. 83, Springer Verlag (2006) 61-82. (PDF)

    62. N. I. M. Gould and Ph. L. Toint, ``Global Convergence of a Non-monotone Trust-Region SQP-Filter Algorithm for Nonlinear Programming''. in ``Multiscale Optimization Methods and Applications'' (W. W. Hager, S.-J. Huang, P. M. Pardalos and O. A. Prokopyev, eds.) Springer Series on Nonconvex Optimization and Its Applications, Vol. 82, Springer Verlag (2006) 125-150. (PDF)

    63. R. H. Byrd, N. I. M. Gould, J. Nocedal and R. A. Waltz, ``On the convergence of successive linear-quadratic programming algorithms''. SIAM Journal on Optimization 16 (2) (2006) 471-489. (PDF)

    64. N. I. M. Gould, C. Sainvitu and Ph. L. Toint, ``A filter-trust-region method for unconstrained optimization'' SIAM Journal on Optimization 16 (2) (2006) 341-357. (PDF)

    65. N. I. M. Gould, D. Orban, A. Sartenaer and Ph. L. Toint, ``Sensitivity of trust-region algorithms to their parameters''. 4OR, 3 (1) (2005) 227-241. (PDF)

    66. J. A. Scott, Y. Hu and N. I. M. Gould, ``An evaluation of sparse direct symmetric solvers: an introduction and preliminary findings'', in ``PARA'04 Workshop on state-of-the-art in scientific computation'' (J. Dongarra, K. Madsen and J. Wasniewski, eds.) Springer LNCS proceedings, (2005) 818-827. (PDF)

    67. N. I. M. Gould, D. Orban and Ph. L. Toint, ``Numerical methods for large-scale nonlinear optimization'' Acta Numerica 14 (2005) 299-361. (PDF)

    68. N. I. M. Gould, S. Leyffer and Ph. L. Toint, ``A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares''. SIAM Journal on Optimization 15 (1) (2005) 17-38. (PDF)

    69. N. I. M. Gould and Ph. L. Toint, ``How mature is nonlinear optimization?'', in Applied mathematics entering the 21st century: invited talks from the ICIAM 2003 Congress (J. M. Hill and R. Moore, eds.), SIAM, Philadelphia (2004) 141-161. (PDF)

    70. N. I. M. Gould and J. A. Scott ``A numerical evaluation of HSL packages for the direct-solution of large sparse, symmetric linear systems of equations''. ACM Transactions on Mathematical Software 30(3) (2004) 300-325. (PDF)

    71. N. I. M. Gould and Ph. L. Toint, ``Preprocessing for quadratic programming'', Mathematical Programming B 100:1 (2004) 95-132. (PDF)

    72. R. H. Byrd, N. I. M. Gould, J. Nocedal and R. A. Waltz ``An active set algorithm for nonlinear programming using linear programming and equality constrained subproblems''. Mathematical Programming B 100:1 (2004) 27-48. (PDF)

    73. N. I. M. Gould and Ph. L. Toint. ``The filter idea and its application to the nonlinear feasibility problem''. In ``Proceedings 20th Biennial Conference on Numerical Analysis'' (D. Griffiths and A. Watson, eds), University of Dundee, Scotland (2003), 73-79. (PDF)

    74. N. I. M. Gould, D. Orban and Ph. L. Toint, ``CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited'', ACM Transactions on Mathematical Software 29(4) (2003) 373-394. (PDF)

    75. N. I. M. Gould, D. Orban and Ph. L. Toint, ``GALAHAD--a library of thread-safe fortran 90 packages for large-scale nonlinear optimization''. ACM Transactions on Mathematical Software 29(4) (2003) 353-372. (PDF)

    76. N. I. M. Gould and Ph. L. Toint, ``Global convergence of a hybrid trust-region SQP-Filter algorithm for general nonlinear programming'', in ``System Modelling and Optimization XX'' (E. W. Sachs and R. Tichatschke, eds) Kluwer Academic Publishers (2003) 23-54. (PDF)

    77. N. I. M. Gould, ``Some Reflections on the Current State of Active-Set and Interior-Point Methods for Constrained Optimization'' SIAG/Optimization Views-and-News 14 (1) (2003) 2-7. (PDF)

    78. N. I. M. Gould and S. Leyffer, ``An introduction to algorithms for nonlinear optimization''. in ``Frontiers in Numerical Analyis (Durham 2002)'', (J. F. Blowey, A. W. Craig and T. Shardlow, eds) Springer Verlag (2003) 109-197. (PDF)

    79. N. I. M. Gould and Ph. L. Toint, ``Numerical methods for large-scale non-convex quadratic programming'', in ``Trends in Industrial and Applied Mathematics''. (A. H. Siddiqi and M. Kocvara, eds) Kluwer Academic Publishers (2002) 149-179. (PDF)

    80. R. Fletcher, N. I. M. Gould, S. Leyffer, Ph. L. Toint and A. Wächter, ``Global convergence of trust-region SQP-filter algorithms for general nonlinear programming''. SIAM Journal on Optimization 13 (2002) 635-659. (PDF)

    81. N. I. M. Gould and Ph. L. Toint, ``An iterative working-set method for large-scale non-convex quadratic programming''. Applied Numerical Mathematics 43 (1-2) (2002) 109-128. (PDF)

    82. N. I. M. Gould, D. Orban, A. Sartenaer and Ph. L. Toint, ``Componentwise fast convergence in the solution of full-rank systems of nonlinear equations''. Mathematical Programming B 92 (2002) 481-508. (PDF)

    83. N. I. M. Gould, M. E. Hribar and J. Nocedal, ``On the solution of equality constrained quadratic programming problems arising in optimization'', SIAM Journal on Scientific Computing 23 (4) (2001) 1375-1394. (PDF)

    84. N. I. M. Gould, D. Orban, A. Sartenaer and Ph. L. Toint, ``Superlinear convergence of primal-dual interior point algorithms for nonlinear programming''. SIAM Journal on Optimization 11 (2001) 974-1002. (PDF)

    85. N. I. M. Gould, S. Lucidi, M. Roma and Ph. L. Toint, ``Exploiting Negative Curvature Directions in Linesearch Methods for Unconstrained Optimization'', Optimization Methods and Software 14 1-2 (2000) 75-98. (PDF)

    86. N. I. M. Gould and Ph. L. Toint, ``SQP methods for large-scale nonlinear programming''. in ``System Modelling and Optimization, Methods, Theory and Applications'' (M. J. D. Powell and S. Scholtes, eds) Kluwer Academic Publishers (2000) 149-178. (PDF)

    87. C. Keller, N. I. M. Gould and A. J. Wathen, ``Constraint preconditioning for indefinite linear systems'', SIAM Journal on Matrix Analysis and Applications 21 (2000) 1300-1317. (PDF)

    88. A. R. Conn, N. I. M. Gould, D. Orban and Ph. L. Toint, ``A primal-dual trust-region algorithm for non-convex nonlinear optimization''. Mathematical Programming 87 (2000) 215-249. (PDF)

    89. N. I. M. Gould ``Iterative methods for ill-conditioned linear systems from optimization'', in ``Nonlinear Optimization and Related Topics'', (G. Di Pillo and F. Giannnessi, eds) Kluwer Academic Publishers (1999) 123-142. (PDF)

    90. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A primal-dual algorithm for minimizing a nonconvex function subject to bound and linear equality constraints'', in ``Nonlinear Optimization and Related Topics'', (G. Di Pillo and F. Giannnessi, eds) Kluwer Academic Publishers (1999) 15-50. (PDF)

    91. M. J. Daydé, J. P. Décamps and N. I. M. Gould, ``Subspace-by-Subspace preconditioners for structured linear systems''. Numerical Linear Algebra 6 (1999) 213-234. (PDF)

    92. N. I. M. Gould and Ph. L. Toint, ``A note on the convergence of barrier algorithms to second-order necessary points'', Mathematical Programming 85 (1999) 433-438. (PDF)

    93. N. I. M. Gould, S. Lucidi, M. Roma and Ph. L. Toint, ``Solving the trust-region subproblem using the Lanczos method'', SIAM Journal on Optimization 9 (1999) 504-525. (PDF)

    94. N. I. M. Gould, ``On modified factorizations for large-scale linearly-constrained optimization''. SIAM Journal on Optimization 9 (1999) 1041-1063. (PDF)

    95. M. J. Daydé, J. P. Décamps and N. I. M. Gould, ``On the Use of Block Stretching for Solving Unassembled Linear Systems'', Calculateurs Paralléles, Réseaux et Systémes Répartis, 10 (4) (1998) 391-399. (PDF)

    96. N. I. M. Gould and J. Nocedal, ``The modified absolute-value factorization norm for trust-region minimization'', in ``High Performance Algorithms and Software in Nonlinear Optimization'' (R. De Leone, A. Murli, P. M. Pardalos and G. Toraldo, eds.), Kluwer Academic Publishers (1998) 225-241. (PDF)

    97. N. I. M. Gould, S. Lucidi, M. Roma and Ph. L. Toint, ``A linesearch algorithm with memory for unconstrained optimization''. in ``High Performance Algorithms and Software in Nonlinear Optimization'' (R. De Leone, A. Murli, P. M. Pardalos and G. Toraldo, eds.), Kluwer Academic Publishers (1998) 207-223. (PDF)

    98. N. I. M. Gould and J. A. Scott, ``Sparse approximate-inverse preconditioners using norm-minimization techniques'', SIAM Journal on Scientific and Statistical Computing 19 (1998) 605-625. (PDF)

    99. M. J. Daydé, J. P. Décamps, J.-Y. L'Excellent and N. I. M. Gould, ``Solution of large scale partially separable unconstrained optimization problems using element-by-element preconditioners'', in ``Proceedings of NAFEMS World Congress 97'', Glasgow, Scotland, Vol. 2 (1997) 942-953. (PDF)

    100. M. J. Daydé, J.-Y. L'Excellent and N. I. M. Gould, ``Element-by-element preconditioners for large partially separable optimization problems'', SIAM Journal on Scientific and Statistical Computing 18 (1997) 1767-1787. (PDF)

    101. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Methods for nonlinear constraints in optimization calculations'', in ``The state of the Art in Numerical Analysis'' (I. S. Duff and A. Watson, eds.), Oxford University Press (1997) 363-390. (PDF)

    102. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds'', Computational Optimization and Applications 7 (1997) 41-69. (PDF)

    103. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds'', Mathematics of Computation 66 (1997) 261-288 and S1-S11. (PDF) (PDF)

    104. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``Convergence properties of minimization algorithms for convex constraints using a structured trust region'', SIAM Journal on Optimization 6 (1996) 1059-1086. (PDF)

    105. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints'' SIAM Journal on Optimization 6 (1996) 674-703. (PDF)

    106. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization'', Mathematical Programming 73 (1996) 73-110. (PDF)

    107. M. J. Daydé, J.-Y. L'Excellent and N. I. M. Gould, ``Preprocessing of sparse unassembled linear systems for efficient solution using element-by-element preconditioners'', in ``Proceedings of Euro-Par 96, Lyons'' (A. M. L. Bourgé, P. Fragniaud and Y. Roberts, eds.) Lecture Notes in Computer Science 1124 Springer-Verlag, Berlin (1996) 34-43. (PDF)

    108. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``On Iterated-Subspace Minimization Methods for Nonlinear Optimization'', in ``Proceedings on Linear and Nonlinear Conjugate Gradient-Related Methods'' (L. Adams and L. Nazareth, eds.), SIAM, Philadelphia (1996) 50-78. (PDF)

    109. M. J. Daydé, J.-Y. L'Excellent and N. I. M. Gould, ``Solution of structured systems of linear equations using element-by-element preconditioners'', in ``Iterative methods in linear algebra, II'' (S. D. Margenov and P. S. Vassilevski, eds.) Volume 3 in the IMACS Series in Computational and Applied Mathematics (1995). (PDF)

    110. I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``CUTE: Constrained and Unconstrained Testing Environment'', ACM Transactions on Mathematical Software 21 (1995) 123-160. (PDF)

    111. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A note on exploiting structure when using slack variables'', Mathematical Programming 67 (1994) 89-98. (PDF)

    112. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization'', Numerische Mathematik 68 (1994) 17-33. (PDF)

    113. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Large-scale nonlinear constrained optimization: a current survey'', in E. Spedicato, editor, Algorithms for continuous optimization: the state of the art. Kluwer Academic Publishers, Dordrecht, The Netherlands, (1994) 287-332. (PDF)

    114. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Improving the decomposition of partially separable functions in the context of large-scale optimization: a first approach'', in Large Scale Optimization: State of the Art (W. W. Hager, D. W. Hearn and P.M. Pardalos, eds.) Kluwer Academic Publishers B.V (1994) 82-94. (PDF)

    115. A. R. Conn, N. I. M. Gould, M. Lescrenier and Ph. L. Toint, ``Performance of a multifrontal scheme for partially separable optimization'', in Advances in numerical partial differential equations and optimization, Proceedings of the sixth Mexico-United States Workshop (S. Gomez and J.P. Hennart and R.A. Tapia, eds.) Kluwer Academic Publishers (1994) 79-96. (PDF)

    116. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints'', SIAM Journal on Optimization 3 (1993) 164-221. (PDF)

    117. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Large-scale nonlinearly constrained optimization'', in ICIAM 1991, Proceedings of the 2nd International Conference on Industrial and Applied Mathematics (R. O'Malley, ed.), SIAM, Philadelphia (1992) 51-70. (PDF)

    118. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear equality constraints and simple bounds'', in Numerical Analysis 1991, Proceedings of the 14th Biennial Conference (D. Griffiths and G. Watson, eds.), Pitman Research Notes in Mathematics 260 (1992) 49-68. (PDF)

    119. N. I. M. Gould, ``An algorithm for large-scale quadratic programming'', IMA Journal of Numerical Analysis 11 (1991) 299-324. (PDF)

    120. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Convergence of Quasi-Newton matrices generated by the symmetric rank-one update'', Mathematical Programming 50 (1991) 177-195. (PDF)

    121. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds'', SIAM Journal on Numerical Analysis 28 (1991) 545-572. (PDF)

    122. I. S. Duff, N. I. M. Gould, J. K. Reid, J. A. Scott and K. Turner, ``The factorization of sparse symmetric indefinite matrices'', IMA Journal of Numerical Analysis 11 (1991) 181-204. (PDF)

    123. N. I. M. Gould, ``On growth in Gaussian elimination with complete pivoting'', SIAM Journal on Matrix Analysis and Applications 12 (1991) 351-364. (PDF)

    124. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project'', in Computing Methods in Applied Sciences and Engineering (R. Glowinski and A. Lichnewsky, eds.), SIAM Proceedings in Applied Mathematics 45 (1990) 42-54. (PDF)

    125. M. Arioli, I. S. Duff, N. I. M. Gould and J. K. Reid, ``The practical use of the Hellerman-Rarick P4 and P5 variant of Erisman et al.'', SIAM Journal on Scientific and Statistical Computing 11 (1990) 913-927. (PDF)

    126. I. S. Duff, N. I. M. Gould, M. Lescrenier and J. K. Reid, ``The multifrontal method in a Parallel Environment'', in Reliable Numerical Computation (M. G. Cox and S. Hammarling, eds.) Oxford University Press, (1990) 93-111. (PDF)

    127. N. I. M. Gould and J. K. Reid, ``New crash procedures for large systems of linear constraints'', Mathematical Programming 45 (1989) 475-501. (PDF)

    128. N. I. M. Gould, ``On the convergence of a sequential penalty function method for constrained minimization'', SIAM Journal on Numerical Analysis 26 (1989) 107-128. (PDF)

    129. N. I. M. Gould, ``On solving three classes of nonlinear programming problems via simple differentiable penalty functions'', Journal of Optimization Theory and Applications 56 (1988) 89-126. (PDF)

    130. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Testing a class of methods for solving minimization problems with simple bounds on the variables'', Mathematics of Computation 50 (1988) 399-430. (PDF)

    131. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Global convergence of a class of trust region algorithms for optimization with simple bounds'', SIAM Journal on Numerical Analysis 25 (1988) 433-460 and 26 (1989) 764-767. (PDF), (PDF)

    132. A. R. Conn and N. I. M. Gould, ``An exact penalty function for semi-infinite programming'', Mathematical Programming 37 (1987) 19-40. (PDF)

    133. N. I. M. Gould, ``On the accurate determination of search directions for simple differentiable penalty functions'', IMA Journal of Numerical Analysis 6 (1986) 357-372. (PDF)

    134. R. J. Caron and N. I. M. Gould, ``Finding a positive semi-definite interval for a parametric matrix'', Linear Algebra and its Applications 76 (1986) 19-29. (PDF)

    135. N. I. M. Gould, ``On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem'', Mathematical Programming 32 (1985) 90-99. (PDF)

    136. A. R. Conn and N. I. M. Gould, ``On the location of directions of infinite descent for nonlinear programming algorithms'', SIAM Journal on Numerical Analysis 21 (1984) 1162-1179. (PDF)

    137. P. E. Gill, N. I. M. Gould, W. Murray, M. A. Saunders and M. H. Wright, ``A Weighted Gram-Schmidt method for convex quadratic programming'', Mathematical Programming 30 (1984) 176-196. (PDF)

Conference proceedings:

      1. C. L. Farmer, J. M. Fowkes and N. I. M. Gould, ``Optimal well placement''. Article B033, ECMOR X11 -- 12th European Conference on the Mathematics of Oil Recovery (2010). (PDF) See also, Technical Report RAL-TR-2010-026 (2010), Rutherford Appleton Laboratory, Chilton, England. (PDF)

      2. C. Cartis and N. I. M. Gould, ``Finding a point in the relative interior of a polyhedron, with applications to compressed sensing''. Proceedings of SPARS'09 (Signal Processing with Adaptive Sparse Structured Representations), Saint-Malo, France (2009). (PDF)

Preprints & Technical reports:

    1. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Strong evaluation comlexity bounds for arbitrary-order optimization of nonconvex nonsmooth composite functions''. Preprint RAL-P-2020-001 (2020), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    2. N. I. M. Gould, T. Rees and J. A. Scott, ``Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints''. Preprint RAL-TR-2019-001 (2019), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    3. N. I. M. Gould, T. Rees and J. A. Scott, ``A higher order method for solving nonlinear least-squares problems''. Preprint RAL-P-2017-010 (2017), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    4. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization''. Preprint RAL-P-2017-007 (2017), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    5. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models''. Preprint RAL-P-2017-006 (2017), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    6. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Evaluation complexity bounds for smooth constrained nonlinear optimisation using scaled KKT conditions, high-order models and the criticality measure Χ''. arXiv:1705.04895 (2017). (PDF)

    7. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models''. Technical Report RAL-TR-2015-011 (2015), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    8. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled {KKT} conditions and high-order models'', Technical Report RAL-TR-2015-010 (2015), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    9. N. I. M. Gould and J. A. Scott, ``The state-of-the-art of preconditioners for sparse linear least-squares problems: the complete results'', Technical Report RAL-TR-2015-009 (2015), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    10. F. E. Curtis, N. I. M. Gould, H. Jiang and D. P. Robinson ``Adaptive augmented Lagrangian methods: algorithms and practical numerical experience--detailed version''. arXiv:1408.4500 (2014). (PDF)

    11. F. E. Curtis, N. I. M. Gould, D. P. Robinson and Ph. L. Toint, ``An interior-point trust-funnel algorithm for nonlinear optimization using a squared-violation feasibility measure''. Technical Report RAL-TR-2014-001 (2014), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    12. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian''. Technical Report RAL-TR-2013-004 (2013), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    13. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods''. Preprint RAL-P-2013-002 (2013), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    14. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``On the complexity of the steepest-descent with exact linesearches''. Technical Report RAL-TR-2012-015 (2012), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    15. C. Cartis, N. I. M. Gould and Ph. L. Toint, ``Optimal Newton-type methods for nonconvex smooth optimization problems''. Technical Report RAL-TR-2011-011 (2011), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    16. N. I. M. Gould, D. P. Robinson and Ph. L. Toint, ``Corrigendum: nonlinear programming without a penalty function or a filter''. Technical Report RAL-TR-2011-006 (2011), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    17. M. Friedlander, N. I. M. Gould, S. Leyffer and T. Munson, ``A filter active-set trust-region method''. Preprint ANL/MCS-P1456-0907, Argonne National Laboratory, Argonne, IL, USA. (PDF)

    18. C. Cartis and N. I. M. Gould, ``Finding a well-centered point within a polyhedron''. Technical Report RAL-TR-2006-016 (2006), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    19. N. I. M. Gould, Y. Hu and J. A. Scott, ``Complete results from a numerical evaluation of sparse direct solvers for the solution of large, sparse, symmetric linear systems of equations''. Numerical Analysis Group Internal Report 2005-1 (2005), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    20. N. I. M. Gould and J. A. Scott ``Complete results from a numerical evaluation of HSL packages for the direct-solution of large sparse, symmetric linear systems of equations''. Numerical Analysis Group Internal Report 2003-2 (2003), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    21. N. I. M. Gould, D. Orban and Ph. L. Toint, ``Results from a numerical evaluation of LANCELOT B''. Numerical Analysis Group Internal Report 2002-1 (2002), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    22. N. I. M. Gould and Ph. L. Toint, ``A Quadratic Programming Bibliography''. Numerical Analysis Group Internal Report 2000-1 (2000), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    23. I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint, ``A numerical comparison between the LANCELOT and MINOS packages for large-scale nonlinear optimization'', Technical Report RAL-TR 97-054 (1997), Rutherford Appleton Laboratory, Chilton, England. (PDF)

    24. M. Arioli, T. F. Chan, I. S. Duff, N. I. M. Gould and J. K. Reid, ``Computing a search direction for large-scale linearly constrained nonlinear optimization calculations'', Technical Report TR/PA/93/34 (1993), CERFACS, Toulouse, France.

    25. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``Local Convergence Properties of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints'', Technical Report TR/PA/93/27 (1993), CERFACS, Toulouse, France.

    26. A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint, ``Global Convergence of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints'', Technical Report TR/PA/93/26 (1993), CERFACS, Toulouse, France.

    27. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``Intensive numerical tests with LANCELOT (Release A): the complete results'' Technical Report 92/15 (1992), Dept. of Mathematics, FUNDP, Namur, Belgium.

    28. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A comprehensive description of LANCELOT'', Technical Report 91/10 (1991), Dept. of Mathematics, FUNDP, Namur, Belgium,

    29. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``An introduction to the standard data input format (SDIF) for nonlinear mathematical programming problems'', Technical Report 91/8 (1991), Dept. of Mathematics, FUNDP, Namur, Belgium.

    30. A. R. Conn, N. I. M. Gould and Ph. L. Toint, ``A proposal for a standard data input format for large-scale nonlinear programming problems'', University of Waterloo report CSS-89-61 (1989) Ontario, Canada.

    31. N. I. M. Gould, ``The stability of the solution of general quadratic programs'', report CORR 83-11, Department of Combinatorics and Optimization, University of Waterloo, Canada (1983)

    32. N. I. M. Gould, ``The generalized steepest-edge for linear programming: part 2, practicalities'', report CORR 84-1, Department of Combinatorics and Optimization, University of Waterloo, Canada (1984)

    33. N. I. M. Gould, ``The generalized steepest-edge for linear programming'', report CORR 83-2, Department of Combinatorics and Optimization, University of Waterloo, Canada (1983)

    34. P. E. Gill, N. I. M. Gould, W. Murray, M. A. Saunders and M. H. Wright, ``A range-space quadratic programming algorithm for problems with a mixture of bounds and general constraints'', Technical report SOL 82-10 (1982) Department of Operations Research, Stanford University, California, U.S.A.

    35. P. E. Gill, N. I. M. Gould, W. Murray, M. A. Saunders and M. H. Wright, ``Range-space methods for convex quadratic programming problems'', Technical report SOL 82-9 (1982) Department of Operations Research, Stanford University, California, U.S.A.

    36. N. I. M. Gould and W. Murray, `` The numerical solution of a problem arising from the accurate determination of an earthquake epicenter occurring in a seismic net'', Stanford University/U.S. Geological Survey (1981).

    37. P. E. Gill, N. I. M. Gould, W. Murray and S. M. Picken, NPL algorithms library reports E/4/11, E/4/12, E/4/17, E/4/18, E/4/23, E/4/24, E/4/25, E/4/57 and E/4/58, National Physical Laboratory, England (1977).

  • GALAHAD - a thread-safe library of Fortran 2003 packages for solving nonlinear optimization problems
  • LANCELOT - a fortran 77 package for solving large-scale nonlinearly constrained optimization problems
  • CUTEst - the latest evolution of CUTE, the constrained and unconstrained testing environment for numerical optimization
  • CUTEr - an earlier version of CUTEst
  • HSL - a collection of state-of-the-art packages for large-scale scientific computation

My course on continuous optimization

I use these sites a great deal, so this is really just for my benefit!