Technical Reports

2022

2020

  • RAL-P-2020-004 (PDF)
    J. Scott and M. Tuma
    A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems
  • RAL-P-2020-003 (PDF)
    J. Scott and M. Tuma
    A null-space approach for symmetric saddle point systems with a non zero (2,2) block
  • RAL-P-2020-002 (PDF)
    T. Rees and M. Wathen
    An element-based preconditioner for mixed finite element problems
  • RAL-P-2020-001 (PDF)
    C. Cartis, N.I.M. Gould, P.L. Toint
    Strong evaluation comlexity bounds for arbitrary-order optimization of nonconvex nonsmooth composite functions

2019

  • RAL-TR-2019-005 (PDF)
    C. Cartis, N.I.M. Gould, M. Lange
    On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces
  • RAL-TR-2019-004 (PDF)
    N.I.M. Gould and V. Simoncini
    Error estimates for iterative algorithms for minimizing regularized quadratic subproblems
  • RAL-TR-2019-003 (PDF)
    T. Davis, I.S. Duff, S. Nakov
    Design and implementation of a parallel Markowitz Threshod Algorithm
  • RAL-TR-2019-001 (PDF)
    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
  • RAL-P-2019-004 (PDF)
    I. Dauzickaite, A.S. Lawless, J.A. Scott, P.J. van Leeuwen
    Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation
  • RAL-P-2019-002 (PDF)
    M. Wathen and C. Greif
    A scalable approximate inverse block preconditioner for an incompressible magnetohydrodynamics model problem
  • RAL-P-2019-001 (PDF)
    J.A. Scott and M. Tuma
    Strengths and limitations of stretching for least-squares problems with some dense rows

2018

  • RAL-P-2018-012 (PDF)
    I. Duff, J. Hogg, F. Lopez
    A new sparse symmetric indefinite solver using a posteriori threshold pivoting
  • RAL-P-2018-006 (PDF)
    C. Cartis, N.I.M. Gould, Ph.L. Toint
    Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints
  • RAL-TR-2018-008 (PDF)
    S. Cayrols, I.S. Duff and F. Lopez
    Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model
  • RAL-P-2018-004 (PDF)
    I.S. Duff, P.A. Knight, L. le Gorrec, S. Mouysset and D. Ruiz
    Uncovering hidden block structure
  • RAL-P-2018-002 (PDF)
    J.A. Scott and M. Tuma
    Sparse stretching for solving sparse-dense linear least-squares problems

2017

  • RAL-TR-2017-010 (PDF)
    I.S. Duff, F. Lopez, S. Nakov
    Sparse Direct Solution on Parallel Computers
  • RAL-P-2017-010 (PDF)
    N.I.M. Gould, T. Rees, J.A. Scott
    A higher order method for solving nonlinear least-squares problems
  • RAL-P-2017-009 (PDF)
    N.I.M. Gould, T. Rees, J.A. Scott
    Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems
  • RAL-P-2017-008 (PDF)
    S. Lungten, W.H.A. Schilders and J.A. Scott
    Preordering saddle-point systems for sparse LDLT factorization without pivoting
  • RAL-P-2017-007 (PDF)
    C. Cartis, N.I.M. Gould, Ph.L. Toint
    Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
  • RAL-TR-2017-006 (PDF)
    I.S. Duff and F. Lopez
    Experiments with sparse Cholesky using a parametrized task graph implementation
  • RAL-P-2017-006 (PDF)
    C. Cartis, N.I.M. Gould, Ph.L. Toint
    Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
  • RAL-P-2017-005 (PDF)
    C. Cartis, N.I.M. Gould, Ph.L. Toint
    Optimality of orders one to three and beyond : characterization and evaluation complexity in constrained nonconvex optimization
  • RAL-TR-2017-003 (PDF)
    I.S. Duff, A.M. Erisman, J.K. Reid
    The Hellerman-Rarick algorithm
  • RAL-P-2017-002 (PDF)
    J.A. Scott and M. Tuma
    A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows
  • RAL-P-2017-003 (PDF)
    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
  • RAL-P-2017-001 (PDF)
    J.A. Scott and M. Tuma
    Solving mixed sparse-dense linear least squares by preconditioned iterative methods

2016

  • RAL-P-2016-016 (PDF)
    I.S. Duff, J. Hogg and F. Lopez
    Experiments with sparse Cholesky using a sequential task-flow implementation
  • RAL-P-2016-010 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    Universal regularization methods-varying the power, the smoothness and the accuracy
  • RAL-P-2016-009 (PDF)
    J. Hogg, J. Hook, J.A. Scott and F. Tisseur
    A max-plus approach to incomplete Cholesky factorization preconditioners
  • RAL-P-2016-008 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    Second-order optimality and beyond: characterization and evaluation complexity in nonconvex convexly-constrained optimization
  • RAL-P-2016-006 (PDF)
    E. Chow and J.A. Scott
    On the use of iterative methods and blocking for solving sparse triangular systems in incomplete factorization preconditioning
  • RAL-P-2016-005 (PDF)
    J.A. Scott
    On using Cholesky-based factorizations for solving rank-deficient sparse linear least-squares problems
  • RAL-P-2016-004 (PDF)
    J.D. Hogg, J.A. Scott and H.S. Thorne
    Numerically-aware orderings for sparse symmetric linear systems
  • RAL-P-2016-003 (PDF)
    N.I.M. Gould and D.P. Robinson
    A dual gradient-projection method for large-scale strictly convex quadratic probems
  • RAL-P-2016-002 (PDF)
    D. Packwood, J.R. Kermode, L. Mones, N. Bernstein, J Woolley, N.I.M. Gould, C. Ortner and G. Csanyi
    A universal preconditioner for simulating condensed phase materials
  • RAL-P-2016-001 (PDF)
    J.A. Scott and M. Tuma
    Preconditioning of linear least squares by RIF for implicitly held normal equations

2015

  • RAL-TR-2015-011 (PDF)
    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
  • RAL-P-2015-010 (PDF)
    N.I.M. Gould and J.A. Scott
    The state-of-the-art of preconditioners for sparse linear least-squares problems
  • RAL-TR-2015-010 (PDF)
    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
  • RAL-TR-2015-009 (PDF)
    N.I.M. Gould and J.A. Scott
    The state-of-the-art of preconditioners for sparse linear least-squares problems: the complete results
  • RAL-P-2015-005 (PDF)
    P. Dunning, E. Ovtchinnikov, J.A. Scott and A. Kim
    Level-set topology optimization with many linear buckling constraints using an efficient robust eigensolver
  • RAL-P-2015-004 (PDF)
    N.I.M. Gould and J.A. Scott
    A note on performance profiles for benchmarking software
  • RAL-P-2015-002 (PDF)
    J.A. Scott and M. Tuma
    Solving symmetric indefinite systems using memory efficient incomplete factorization preconditioners

2014

  • RAL-P-2014-016 (PDF)
    T. Rees and J.A. Scott
    The null-space method and its relationship with matrix factorizations for sparse saddle point systems
  • RAL-P-2014-014 (PDF)
    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
  • RAL-P-2014-013 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    Corrigendum: On the complexity of finding first-order critical pointsb in constrained nonlinear optimization
  • RAL-P-2014-012 (PDF)
    N.I.M. Gould, Y. Loh and D.P. Robinson
    A filter SQP method : local convergence and numerical results
  • RAL-P-2014-011 (PDF)
    F.E. Curtis, N.I.M. Gould, H. Jiang and D.P. Robinson
    Adapting augmented Lagrangian methods: algorithms and practical numerical experience
  • RAL-TR-2014-011 (PDF)
    J.A. Scott
    "Experiments using incomplete Cholesky factorization preconditioners for saddle-point systems arising in interior-point methods"
  • RAL-TR-2014-006 (PDF)
    N.I.M. Gould, C. Ortner and D. Packwood
    An efficient dimer method with preconditioning and linesearch
  • RAL-P-2014-007 (PDF)
    M. Arioli and I.S. Duff
    Preconditioning of linear least-squares problems by identifying basic variables
  • RAL-P-2014-006 (PDF)
    J.D. Hogg, E. Ovtchinnikov and J.A. Scott
    A sparse symmetric indefinite direct solver for GPU architectures
  • RAL-P-2014-005 (PDF)
    L.A. Drummond, I.S. Duff, R. Guivarch, D. Ruiz, and M. Zenadi
    Partitioning strategies for the Block Cimmino algorithm
  • RAL-P-2014-004 (PDF)
    O. Kaya, E. Kayaaslan, B. Uçar, and I.S. Duff
    Fill-in reduction in sparse matrix factorizations using hypergraphs
  • RAL-P-2014-003 (PDF)
    J.A. Scott and M. Tůma
    On signed incomplete Cholesky factorization preconditioners for saddle-point systems
  • RAL-P-2014-002 (PDF)
    J.D. Hogg and J.A. Scott
    On the efficient scaling of sparse symmetric matrices using an auction algorithm
  • RAL-P-2014-001 (PDF)
    F. E. Curtis, N.I.M. Gould, D.P. Robinson and Ph.L. Toint
    An interior-point trust-funnel algorithm for nonlinear optimization
  • RAL-TR-2014-001 (PDF)
    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

2013

2012

2011

  • RAL-TR-2011-026 (PDF)
    M. Arioli, I.S. Duff, J.D. Hogg and H.S. Thorne
    Guidelines for the development of MATLAB interfaces for HSL packages (revised for MATLAB 2011a)
  • RAL-TR-2011-024 (PDF)
    J.D. Hogg and J.A. Scott
    HSL_MA97 : a bit-compatible multifrontal code for sparse symmetric systems
  • RAL-TR-2011-023 (PDF)
    I.S. Duff
    European Exascale Software Initiative: numerical libraries, solvers, and algorithms
  • RAL-TR-2011-022 (PDF)
    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
  • RAL-TR-2011-020 (PDF)
    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
  • RAL-TR-2011-019 (PDF)
    J.A. Scott and Y. Hu
    Level-based heuristics and hill climbing for the antibandwidth maximization problem
  • RAL-TR-2011-017 (PDF)
    N.I.M. Gould, D. Orban and D.P. Robinson
    Trajectory-following methods for large-scale degenerate quadratic programming
  • RAL-TR-2011-016 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
  • RAL-TR-2011-015 (PDF)
    J.D. Hogg, J.K. Reid and J.A. Scott
    Guidelines for the development of HSL software, 2011 version
  • RAL-TR-2011-011 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    Optimal Newton-type methods for nonconvex smooth optimization problems
  • RAL-TR-2011-010 (PDF)
    M. Arioli and J.A. Scott
    Chebyshev acceleration of iterative refinement
  • RAL-TR-2011-009 (PDF)
    N.I.M. Gould
    How good are extrapolated bi-projection methods for linear feasibility problems?
  • RAL-TR-2011-008 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    On the complexity of finding first-order critical points in constrained nonlinear optimization
  • RAL-TR-2011-007 (PDF)
    N.I.M. Gould, M. Porcelli and Ph.L. Toint
    Updating the regularization parameter in the adaptive cubic regularization algorithm
  • RAL-TR-2011-006 (PDF)
    N.I.M. Gould, D.P. Robinson and Ph.L. Toint
    Corrigendum: nonlinear programming without a penalty function or a filter
  • RAL-TR-2011-005 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
  • RAL-TR-2011-002 (PDF)
    C. Cartis, N.I.M. Gould and Ph.L. Toint
    Complexity bounds for second-order optimality in unconstrained optimization
  • RAL-P-2011-001 (PDF)
    I.S. Duff and K. Kaya
    Preconditioners based on strong components

2010

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2008

2007

2006

2005

2004

2003

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1970 - 1990


The group has also issued the following Numerical Analysis Group Internal Reports: