Nicholas I. M. Gould

Publication Activity (10 Years)

Years Active: 1984-2024
Publications (10 Years): 16

Top Topics

Regularization Methods

Nonlinear Optimization

Solving Nonlinear

Linear Least Squares

Top Venues

Comput. Optim. Appl.

Optim. Methods Softw.

Publications

Jaroslav M. Fowkes, Nicholas I. M. Gould, Jennifer A. Scott
Approximating sparse Hessian matrices using large-scale linear least squares. Numer. Algorithms 96 (4) (2024)
Jaroslav M. Fowkes, Nicholas I. M. Gould
GALAHAD 4.0: an open source library of Fortran packages with C and Matlab interfaces for continuous optimization. J. Open Source Softw. 8 (87) (2023)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Sharp Worst-Case Evaluation Complexity Bounds for Arbitrary-Order Nonconvex Optimization with Inexpensive Constraints. SIAM J. Optim. 30 (1) (2020)
Nicholas I. M. Gould, Valeria Simoncini
Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. Optim. Methods Softw. 35 (2) (2020)
Nicholas I. M. Gould, Tyrone Rees, Jennifer A. Scott
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems. Comput. Optim. Appl. 73 (1) (2019)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization. J. Complex. 53 (2019)
Nicholas I. M. Gould, Daniel P. Robinson
A dual gradient-projection method for large-scale strictly convex quadratic problems. Comput. Optim. Appl. 67 (1) (2017)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization. Math. Program. 161 (1-2) (2017)
Nicholas I. M. Gould, Jennifer A. Scott
The State-of-the-Art of Preconditioners for Sparse Linear Least-Squares Problems. ACM Trans. Math. Softw. 43 (4) (2017)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Optim. Methods Softw. 32 (6) (2017)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. CoRR (2017)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization. CoRR (2017)
Frank E. Curtis, Nicholas I. M. Gould, Daniel P. Robinson, Philippe L. Toint
An interior-point trust-funnel algorithm for nonlinear optimization. Math. Program. 161 (1-2) (2017)
Nicholas I. M. Gould, Jennifer A. Scott
A Note on Performance Profiles for Benchmarking Software. ACM Trans. Math. Softw. 43 (2) (2016)
Frank E. Curtis, Nicholas I. M. Gould, Hao Jiang, Daniel P. Robinson
Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. Optim. Methods Softw. 31 (1) (2016)
Nicholas I. M. Gould, Christoph Ortner, D. Packwood
A dimer-type saddle search algorithm with preconditioning and linesearch. Math. Comput. 85 (302) (2016)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
On the Evaluation Complexity of Constrained Nonlinear Least-Squares and General Constrained Nonlinear Optimization Using Second-Order Methods. SIAM J. Numer. Anal. 53 (2) (2015)
Nicholas I. M. Gould, Yueling Loh, Daniel P. Robinson
A Nonmonotone Filter SQP Method: Local Convergence and Numerical Results. SIAM J. Optim. 25 (3) (2015)
Nicholas I. M. Gould, Dominique Orban, Philippe L. Toint
CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization. Comput. Optim. Appl. 60 (3) (2015)
Daniel Bienstock, Philip E. Gill, Nicholas I. M. Gould
A note on "On fast trust region methods for quadratic models with linear constraints", by Michael J.D. Powell. Math. Program. Comput. 7 (3) (2015)
Coralia Cartis, Jaroslav M. Fowkes, Nicholas I. M. Gould
Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties. J. Glob. Optim. 61 (3) (2015)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
On the complexity of finding first-order critical points in constrained nonlinear optimization. Math. Program. 144 (1-2) (2014)
Nicholas I. M. Gould, Dominique Orban, Tyrone Rees
Projected Krylov Methods for Saddle-Point Systems. SIAM J. Matrix Anal. Appl. 35 (4) (2014)
Nicholas I. M. Gould, Yueling Loh, Daniel P. Robinson
A Filter Method with Unified Step Computation for Nonlinear Optimization. SIAM J. Optim. 24 (1) (2014)
Jaroslav M. Fowkes, Nicholas I. M. Gould, Chris L. Farmer
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. J. Glob. Optim. 56 (4) (2013)
Coralia Cartis, Nicholas I. M. Gould, Philippe 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 J. Optim. 23 (3) (2013)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function. Optim. Methods Softw. 28 (3) (2013)
Nicholas I. M. Gould, Dominique Orban, Daniel P. Robinson
Trajectory-following methods for large-scale degenerate convex quadratic programming. Math. Program. Comput. 5 (2) (2013)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization. SIAM J. Optim. 22 (1) (2012)
Nicholas I. M. Gould, Margherita Porcelli, Philippe L. Toint
Updating the regularization parameter in the adaptive cubic regularization algorithm. Comput. Optim. Appl. 53 (1) (2012)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Optim. Methods Softw. 27 (2) (2012)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Complexity bounds for second-order optimality in unconstrained optimization. J. Complex. 28 (1) (2012)
Nicholas I. M. Gould
How good are extrapolated bi-projection methods for linear feasibility problems? Comput. Optim. Appl. 51 (3) (2012)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming. SIAM J. Optim. 21 (4) (2011)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program. 127 (2) (2011)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity. Math. Program. 130 (2) (2011)
Nicholas I. M. Gould, Philippe L. Toint
Nonlinear programming without a penalty function or a filter. Math. Program. 122 (1) (2010)
Nicholas I. M. Gould, Daniel P. Robinson
A Second Derivative SQP Method: Global Convergence. SIAM J. Optim. 20 (4) (2010)
H. Sue Dollar, Nicholas I. M. Gould, Martin Stoll, Andrew J. Wathen
Preconditioning Saddle-Point Systems with Applications in Optimization. SIAM J. Sci. Comput. 32 (1) (2010)
Nicholas I. M. Gould, Daniel P. Robinson, H. Sue Thorne
On solving trust-region and other regularised subproblems in optimization. Math. Program. Comput. 2 (1) (2010)
Nicholas I. M. Gould, Daniel P. Robinson
A Second Derivative SQP Method: Local Convergence and Practical Issues. SIAM J. Optim. 20 (4) (2010)
Stefania Bellavia, Coralia Cartis, Nicholas I. M. Gould, Benedetta Morini, Philippe L. Toint
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares. SIAM J. Numer. Anal. 48 (1) (2010)
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems. SIAM J. Optim. 20 (6) (2010)
Nicholas I. M. Gould, Valeria Simoncini
Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks. SIAM J. Matrix Anal. Appl. 31 (3) (2009)
Nicholas I. M. Gould
How good are projection methods for convex feasibility problems? Comput. Optim. Appl. 40 (1) (2008)
Nicholas I. M. Gould, Philippe L. Toint
FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems. ACM Trans. Math. Softw. 33 (1) (2007)
Nicholas I. M. Gould, Jennifer A. Scott, Yifan Hu
A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. ACM Trans. Math. Softw. 33 (2) (2007)
H. Sue Dollar, Nicholas I. M. Gould, Wil H. A. Schilders, Andy J. Wathen
Using constraint preconditioners with regularized saddle-point problems. Comput. Optim. Appl. 36 (2-3) (2007)
H. Sue Dollar, Nicholas I. M. Gould, Wil H. A. Schilders, Andrew J. Wathen
Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems. SIAM J. Matrix Anal. Appl. 28 (1) (2006)
Nicholas I. M. Gould, Dominique Orban, Annick Sartenaer, Philippe L. Toint
Sensitivity of trust-region algorithms to their parameters. 4OR 3 (3) (2005)
Richard H. Byrd, Nicholas I. M. Gould, Jorge Nocedal, Richard A. Waltz
On the Convergence of Successive Linear-Quadratic Programming Algorithms. SIAM J. Optim. 16 (2) (2005)
Richard H. Byrd, Nicholas I. M. Gould, Jorge Nocedal, Richard A. Waltz
An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Math. Program. 100 (1) (2004)
Nicholas I. M. Gould, Sven Leyffer, Philippe L. Toint
A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares. SIAM J. Optim. 15 (1) (2004)
Nicholas I. M. Gould, Jennifer A. Scott
A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. ACM Trans. Math. Softw. 30 (3) (2004)
Jennifer A. Scott, Yifan Hu, Nicholas I. M. Gould
An Evaluation of Sparse Direct Symmetric Solvers: An Introduction and Preliminary Findings. PARA (2004)
Nicholas I. M. Gould, Dominique Orban, Philippe L. Toint
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29 (4) (2003)
Nicholas I. M. Gould, Dominique Orban, Philippe L. Toint
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29 (4) (2003)
Nicholas I. M. Gould, Dominique Orban, Annick Sartenaer, Philippe L. Toint
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Math. Program. 92 (3) (2002)
Roger Fletcher, Nicholas I. M. Gould, Sven Leyffer, Philippe L. Toint, Andreas Wächter
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming. SIAM J. Optim. 13 (3) (2002)
Nicholas I. M. Gould, Mary E. Hribar, Jorge Nocedal
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization. SIAM J. Sci. Comput. 23 (4) (2001)
Nicholas I. M. Gould, Philippe L. Toint
Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming. System Modelling and Optimization (2001)
Nicholas I. M. Gould, Dominique Orban, Annick Sartenaer, Philippe L. Toint
Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming. SIAM J. Optim. 11 (4) (2001)
Andrew R. Conn, Nicholas I. M. Gould, Dominique Orban, Philippe L. Toint
A primal-dual trust-region algorithm for non-convex nonlinear programming. Math. Program. 87 (2) (2000)
Carsten Keller, Nicholas I. M. Gould, Andrew J. Wathen
Constraint Preconditioning for Indefinite Linear Systems. SIAM J. Matrix Anal. Appl. 21 (4) (2000)
Nicholas I. M. Gould, Stefano Lucidi, Massimo Roma, Philippe L. Toint
Solving the Trust-Region Subproblem using the Lanczos Method. SIAM J. Optim. 9 (2) (1999)
Nicholas I. M. Gould, Philippe L. Toint
SQP Methods for Large-Scale Nonlinear Programming. System Modelling and Optimization (1999)
Nicholas I. M. Gould, Philippe L. Toint
A note on the convergence of barrier algorithms to second-order necessary points. Math. Program. 85 (2) (1999)
Michel J. Daydé, Jérôme P. Décamps, Nicholas I. M. Gould
Subspace-by-subspace preconditioners for structured linear systems. Numer. Linear Algebra Appl. 6 (3) (1999)
Nicholas I. M. Gould, Jennifer A. Scott
Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques. SIAM J. Sci. Comput. 19 (2) (1998)
Andrew R. Conn, Nicholas I. M. Gould, Philippe 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. Comput. Optim. Appl. 7 (1) (1997)
Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. Math. Comput. 66 (217) (1997)
Michel J. Daydé, Jean-Yves L'Excellent, Nicholas I. M. Gould
Element-by-Element Preconditioners for Large Partially Separable Optimization Problems. SIAM J. Sci. Comput. 18 (6) (1997)
Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization. Math. Program. 73 (1996)
Andrew R. Conn, Nicholas I. M. Gould, Annick Sartenaer, Philippe L. Toint
Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints. SIAM J. Optim. 6 (3) (1996)
Michel J. Daydé, Jean-Yves L'Excellent, Nicholas I. M. Gould
Preprocessing of Sparse Unassembled Linear Systems for Efficient Solution Using Element-by-Element Preconditioners. Euro-Par, Vol. II (1996)
Ingrid Bongartz, Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
CUTE: Constrained and Unconstrained Testing Environment. ACM Trans. Math. Softw. 21 (1) (1995)
Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
A note on exploiting structure when using slack variables. Math. Program. 67 (1994)
Andrew R. Conn, Nicholas I. M. Gould, Philippe L. Toint
Convergence of quasi-Newton matrices generated by the symmetric rank one update. Math. Program. 50 (1991)
Nicholas I. M. Gould, John K. Reid
New crash procedures for large systems of linear constraints. Math. Program. 45 (1-3) (1989)
Andrew R. Conn, Nicholas I. M. Gould
An exact penalty function for semi-infinite programming. Math. Program. 37 (1) (1987)
Nicholas I. M. Gould
On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. Math. Program. 32 (1) (1985)
Philip E. Gill, Nicholas I. M. Gould, Walter Murray, Michael A. Saunders, Margaret H. Wright
A weighted gram-schmidt method for convex quadratic programming. Math. Program. 30 (2) (1984)