A weighted gram-schmidt method for convex quadratic programming. - Philip E. Gill; Nicholas I. M. Gould; Walter Murray; Michael A. Saunders; Margaret H. Wright (Math. Program., 1984)

On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. - Nicholas I. M. Gould (Math. Program., 1985)

An exact penalty function for semi-infinite programming. - Andrew R. Conn; Nicholas I. M. Gould (Math. Program., 1987)

New crash procedures for large systems of linear constraints. - Nicholas I. M. Gould; John K. Reid (Math. Program., 1989)

Use of the P4 and P5 Algorithms for In-Core Factorization of Sparse Matrices. - Mario Arioli; Iain S. Duff; Nick I. M. Gould; John K. Reid (SIAM J. Sci. Comput., 1990)

Convergence of quasi-Newton matrices generated by the symmetric rank one update. - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 1991)

Global Convergence of a Class of Trust Region Algorithms for Optimization Using Inexact Projections on Convex Constraints. - Andrew R. Conn; Nick I. M. Gould; Annick Sartenaer; Philippe L. Toint (SIAM J. Optim., 1993)

A note on exploiting structure when using slack variables. - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 1994)

CUTE: Constrained and Unconstrained Testing Environment. - Ingrid Bongartz; Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (ACM Trans. Math. Softw., 1995)

Preprocessing of Sparse Unassembled Linear Systems for Efficient Solution Using Element-by-Element Preconditioners. - Michel J. Daydé; Jean-Yves L'Excellent; Nicholas I. M. Gould (Euro-Par, Vol. II, 1996)

Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization. - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 1996)

Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints. - Andrew R. Conn; Nicholas I. M. Gould; Annick Sartenaer; Philippe L. Toint (SIAM J. Optim., 1996)

Convergence Properties of Minimization Algorithms for Convex Constraints Using a Structured Trust Region. - Andrew R. Conn; Nick I. M. Gould; Annick Sartenaer; Philippe L. Toint (SIAM J. Optim., 1996)

On the Number of Inner Iterations Per Outer Iteration of a Globally Convergent Algorithm for Optimization with General Nonlinear Inequality Constraints and Simple Bounds. - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (Comput. Optim. Appl., 1997)

A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (Math. Comput., 1997)

Element-by-Element Preconditioners for Large Partially Separable Optimization Problems. - Michel J. Daydé; Jean-Yves L'Excellent; Nicholas I. M. Gould (SIAM J. Sci. Comput., 1997)

Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques. - Nicholas I. M. Gould; Jennifer A. Scott (SIAM J. Sci. Comput., 1998)

SQP Methods for Large-Scale Nonlinear Programming. - Nicholas I. M. Gould; Philippe L. Toint (System Modelling and Optimization, 1999)

A note on the convergence of barrier algorithms to second-order necessary points. - Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 1999)

Subspace-by-subspace preconditioners for structured linear systems. - Michel J. Daydé; Jérôme P. Décamps; Nicholas I. M. Gould (Numer. Linear Algebra Appl., 1999)

On Modified Factorizations for Large-Scale Linearly Constrained Optimization. - Nicholas Ian Mark Gould (SIAM J. Optim., 1999)

Solving the Trust-Region Subproblem using the Lanczos Method. - Nicholas I. M. Gould; Stefano Lucidi; Massimo Roma; Philippe L. Toint (SIAM J. Optim., 1999)

Trust Region Methods - Andrew R. Conn; Nicholas I. M. Gould; Philippe L. Toint (SIAM, 2000)

A primal-dual trust-region algorithm for non-convex nonlinear programming. - Andrew R. Conn; Nicholas I. M. Gould; Dominique Orban; Philippe L. Toint (Math. Program., 2000)

Constraint Preconditioning for Indefinite Linear Systems. - Carsten Keller; Nicholas I. M. Gould; Andrew J. Wathen (SIAM J. Matrix Anal. Appl., 2000)

Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming. - Nicholas I. M. Gould; Philippe L. Toint (System Modelling and Optimization, 2001)

Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming. - Nicholas I. M. Gould; Dominique Orban; Annick Sartenaer; Philippe L. Toint (SIAM J. Optim., 2001)

On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization. - Nicholas I. M. Gould; Mary E. Hribar; Jorge Nocedal (SIAM J. Sci. Comput., 2001)

Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. - Nicholas I. M. Gould; Dominique Orban; Annick Sartenaer; Philippe L. Toint (Math. Program., 2002)

Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming. - Roger Fletcher; Nicholas I. M. Gould; Sven Leyffer; Philippe L. Toint; Andreas Wächter (SIAM J. Optim., 2002)

GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. - Nicholas I. M. Gould; Dominique Orban; Philippe L. Toint (ACM Trans. Math. Softw., 2003)

CUTEr and SifDec: A constrained and unconstrained testing environment, revisited. - Nicholas I. M. Gould; Dominique Orban; Philippe L. Toint (ACM Trans. Math. Softw., 2003)

An Evaluation of Sparse Direct Symmetric Solvers: An Introduction and Preliminary Findings. - Jennifer A. Scott; Yifan Hu 001; Nicholas I. M. Gould (PARA, 2004)

An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. - Richard H. Byrd; Nicholas I. M. Gould; Jorge Nocedal; Richard A. Waltz (Math. Program., 2004)

Nonlinear programming: theory and practice. - Nick I. M. Gould; Sven Leyffer; Philippe L. Toint (Math. Program., 2004)

Preprocessing for quadratic programming. - Nick I. M. Gould; Philippe L. Toint (Math. Program., 2004)

A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares. - Nicholas I. M. Gould; Sven Leyffer; Philippe L. Toint (SIAM J. Optim., 2004)

A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. - Nicholas I. M. Gould; Jennifer A. Scott (ACM Trans. Math. Softw., 2004)

Sensitivity of trust-region algorithms to their parameters. - Nicholas I. M. Gould; Dominique Orban; Annick Sartenaer; Philippe L. Toint (4OR, 2005)

On the Convergence of Successive Linear-Quadratic Programming Algorithms. - Richard H. Byrd; Nicholas I. M. Gould; Jorge Nocedal; Richard A. Waltz (SIAM J. Optim., 2005)

A Filter-Trust-Region Method for Unconstrained Optimization. - Nick I. M. Gould; Caroline Sainvitu; Philippe L. Toint (SIAM J. Optim., 2005)

Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems. - H. Sue Dollar; Nicholas I. M. Gould; Wil H. A. Schilders; Andrew J. Wathen (SIAM J. Matrix Anal. Appl., 2006)

Using constraint preconditioners with regularized saddle-point problems. - H. Sue Dollar; Nicholas I. M. Gould; Wil H. A. Schilders; Andy J. Wathen (Comput. Optim. Appl., 2007)

A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. - Nicholas I. M. Gould; Jennifer A. Scott; Yifan Hu 001 (ACM Trans. Math. Softw., 2007)

FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems. - Nicholas I. M. Gould; Philippe L. Toint (ACM Trans. Math. Softw., 2007)

How good are projection methods for convex feasibility problems? - Nicholas I. M. Gould (Comput. Optim. Appl., 2008)

Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks. - Nicholas I. M. Gould; Valeria Simoncini (SIAM J. Matrix Anal. Appl., 2009)

Nonlinear programming without a penalty function or a filter. - Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 2010)

On solving trust-region and other regularised subproblems in optimization. - Nicholas I. M. Gould; Daniel P. Robinson; H. Sue Thorne (Math. Program. Comput., 2010)

On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2010)

A Second Derivative SQP Method: Global Convergence. - Nicholas I. M. Gould; Daniel P. Robinson (SIAM J. Optim., 2010)

A Second Derivative SQP Method: Local Convergence and Practical Issues. - Nicholas I. M. Gould; Daniel P. Robinson (SIAM J. Optim., 2010)

Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares. - Stefania Bellavia; Coralia Cartis; Nicholas I. M. Gould; Benedetta Morini; Philippe L. Toint (SIAM J. Numer. Anal., 2010)

Preconditioning Saddle-Point Systems with Applications in Optimization. - H. Sue Dollar; Nicholas I. M. Gould; Martin Stoll; Andrew J. Wathen (SIAM J. Sci. Comput., 2010)

Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 2011)

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 2011)

On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2011)

How good are extrapolated bi-projection methods for linear feasibility problems? - Nicholas I. M. Gould (Comput. Optim. Appl., 2012)

Updating the regularization parameter in the adaptive cubic regularization algorithm. - Nicholas I. M. Gould; Margherita Porcelli; Philippe L. Toint (Comput. Optim. Appl., 2012)

Complexity bounds for second-order optimality in unconstrained optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (J. Complex., 2012)

Erratum to: Nonlinear programming without a penalty function or a filter. - Nick I. M. Gould; Philippe L. Toint (Math. Program., 2012)

Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Optim. Methods Softw., 2012)

On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2012)

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. - Jaroslav M. Fowkes; Nicholas I. M. Gould; Chris L. Farmer (J. Glob. Optim., 2013)

Trajectory-following methods for large-scale degenerate convex quadratic programming. - Nicholas I. M. Gould; Dominique Orban; Daniel P. Robinson (Math. Program. Comput., 2013)

A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Optim. Methods Softw., 2013)

On the Evaluation Complexity of Cubic Regularization Methods for Potentially Rank-Deficient Nonlinear Least-Squares Problems and Its Relevance to Constrained Nonlinear Optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2013)

On the complexity of finding first-order critical points in constrained nonlinear optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 2014)

A Filter Method with Unified Step Computation for Nonlinear Optimization. - Nicholas I. M. Gould; Yueling Loh; Daniel P. Robinson (SIAM J. Optim., 2014)

Projected Krylov Methods for Saddle-Point Systems. - Nicholas I. M. Gould; Dominique Orban; Tyrone Rees (SIAM J. Matrix Anal. Appl., 2014)

CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization. - Nicholas I. M. Gould; Dominique Orban; Philippe L. Toint (Comput. Optim. Appl., 2015)

Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties. - Coralia Cartis; Jaroslav M. Fowkes; Nicholas I. M. Gould (J. Glob. Optim., 2015)

A note on "On fast trust region methods for quadratic models with linear constraints", by Michael J.D. Powell. - Daniel Bienstock; Philip E. Gill; Nicholas I. M. Gould (Math. Program. Comput., 2015)

A Nonmonotone Filter SQP Method: Local Convergence and Numerical Results. - Nicholas I. M. Gould; Yueling Loh; Daniel P. Robinson (SIAM J. Optim., 2015)

On the Evaluation Complexity of Constrained Nonlinear Least-Squares and General Constrained Nonlinear Optimization Using Second-Order Methods. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Numer. Anal., 2015)

A dimer-type saddle search algorithm with preconditioning and linesearch. - Nicholas I. M. Gould; Christoph Ortner; D. Packwood (Math. Comput., 2016)

Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. - Frank E. Curtis; Nicholas I. M. Gould; Hao Jiang; Daniel P. Robinson (Optim. Methods Softw., 2016)

A Note on Performance Profiles for Benchmarking Software. - Nicholas I. M. Gould; Jennifer A. Scott (ACM Trans. Math. Softw., 2016)

A dual gradient-projection method for large-scale strictly convex quadratic problems. - Nicholas I. M. Gould; Daniel P. Robinson (Comput. Optim. Appl., 2017)

Evaluation complexity bounds for smooth constrained nonlinear optimisation using scaled KKT conditions, high-order models and the criticality measure $χ$. - Coralia Cartis; Nick I. M. Gould; Philippe L. Toint (CoRR, 2017)

Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (CoRR, 2017)

Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Math. Program., 2017)

An interior-point trust-funnel algorithm for nonlinear optimization. - Frank E. Curtis; Nicholas I. M. Gould; Daniel P. Robinson; Philippe L. Toint (Math. Program., 2017)

Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (Optim. Methods Softw., 2017)

The State-of-the-Art of Preconditioners for Sparse Linear Least-Squares Problems. - Nicholas I. M. Gould; Jennifer A. Scott (ACM Trans. Math. Softw., 2017)

Second-Order Optimality and Beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization. - Coralia Cartis; Nick I. M. Gould; Philippe L. Toint (Found. Comput. Math., 2018)

Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems. - Nicholas I. M. Gould; Tyrone Rees; Jennifer A. Scott (Comput. Optim. Appl., 2019)

Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (J. Complex., 2019)

Universal Regularization Methods: Varying the Power, the Smoothness and the Accuracy. - Coralia Cartis; Nick I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2019)

A concise second-order complexity analysis for unconstrained optimization using high-order regularized models. - Coralia Cartis; Nick I. M. Gould; Philippe L. Toint (Optim. Methods Softw., 2020)

Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. - Nicholas I. M. Gould; Valeria Simoncini (Optim. Methods Softw., 2020)

Sharp Worst-Case Evaluation Complexity Bounds for Arbitrary-Order Nonconvex Optimization with Inexpensive Constraints. - Coralia Cartis; Nicholas I. M. Gould; Philippe L. Toint (SIAM J. Optim., 2020)

GALAHAD 4.0: an open source library of Fortran packages with C and Matlab interfaces for continuous optimization. - Jaroslav M. Fowkes; Nicholas I. M. Gould (J. Open Source Softw., 2023)

Approximating sparse Hessian matrices using large-scale linear least squares. - Jaroslav M. Fowkes; Nicholas I. M. Gould; Jennifer A. Scott (Numer. Algorithms, 2024)

Approximating Large-Scale Hessian Matrices Using Secant Equations. - Jaroslav M. Fowkes; Nicholas I. M. Gould; Jennifer A. Scott (ACM Trans. Math. Softw., 2025)