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Gould, Nicholas Ian Mark

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Author ID: gould.nicholas-ian-mark Recent zbMATH articles by "Gould, Nicholas Ian Mark"
Published as: Gould, Nicholas I. M.; Gould, Nicholas Ian Mark; Gould, N. I. M.; Gould, Nicholas
Documents Indexed: 106 Publications since 1984, including 2 Books
Co-Authors: 42 Co-Authors with 94 Joint Publications
1,076 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

101 Publications have been cited 2,679 times in 1,723 Documents Cited by Year
Trust-region methods. Zbl 0958.65071
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
567
2000
CUTE: Constrained and unconstrained testing environment. Zbl 0886.65058
Bongartz, I.; Conn, A. R.; Gould, N.; Toint, Ph. L.
314
1995
CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. Zbl 1068.90526
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
268
2003
Constraint preconditioning for indefinite linear systems. Zbl 0960.65052
Keller, Carsten; Gould, Nicholas I. M.; Wathen, Andrew J.
168
2000
A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. Zbl 0724.65067
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
162
1991
CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Zbl 1325.90004
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
128
2015
Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. Zbl 1038.90076
Fletcher, Roger; Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.; Wächter, Andreas
118
2002
Adaptive cubic regularisation methods for unconstrained optimization. I: Motivation, convergence and numerical results. Zbl 1229.90192
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
111
2011
Adaptive cubic regularisation methods for unconstrained optimization. II: Worst-case function- and derivative-evaluation complexity. Zbl 1229.90193
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
105
2011
Global convergence of a class of trust region algorithms for optimization with simple bounds. Zbl 0643.65031
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
99
1988
Solving the trust-region subproblem using the Lanczos method. Zbl 1047.90510
Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L.
94
1999
On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. Zbl 1211.90225
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
79
2010
On the solution of equality constrained quadratic programming problems arising in optimization. Zbl 0999.65050
Gould, Nicholas I. M.; Hribar, Mary E.; Nocedal, Jorge
76
2001
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. Zbl 1068.90525
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
66
2003
Convergence of quasi-Newton matrices generated by the symmetric rank one update. Zbl 0737.90062
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
56
1991
Testing a class of methods for solving minimization problems with simple bounds on the variables. Zbl 0645.65033
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
51
1988
A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. Zbl 1075.65075
Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.
47
2004
Nonlinear programming without a penalty function or a filter. Zbl 1216.90069
Gould, N. I. M.; Toint, Ph. L.
42
2010
On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. Zbl 1236.90118
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
38
2011
On solving trust-region and other regularised subproblems in optimization. Zbl 1193.65098
Gould, Nicholas I. M.; Robinson, Daniel P.; Thorne, H. Sue
36
2010
Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints. Zbl 0856.90098
Conn, A. R.; Gould, N.; Sartenaer, A.; Toint, Ph. L.
36
1996
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity. Zbl 1267.65061
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
33
2012
On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. Zbl 0591.90068
Gould, Nicholas I. M.
32
1985
A note on performance profiles for benchmarking software. Zbl 1369.65202
Gould, Nicholas; Scott, Jennifer
29
2016
Complexity bounds for second-order optimality in unconstrained optimization. Zbl 1245.65063
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
28
2012
Exploiting negative curvature directions in linesearch methods for unconstrained optimization. Zbl 0988.90039
Gould, N. I. M.; Lucidi, S.; Roma, M.; Toint, Ph. L.
28
2000
Sparse approximate-inverse preconditioners using norm-minimization techniques. Zbl 0911.65037
Gould, Nicholas I. M.; Scott, Jennifer A.
27
1998
The factorization of sparse symmetric indefinite matrices. Zbl 0739.65018
Duff, I. S.; Gould, N. I. M.; Reid, J. K.; Scott, J. A.
23
1991
On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization. Zbl 1250.90083
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
22
2012
Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems. Zbl 1104.65310
Dollar, H. Sue; Gould, Nicholas I. M.; Schilders, Wil H. A.; Wathen, Andrew J.
22
2006
An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Zbl 1146.90513
Byrd, Richard H.; Gould, Nicholas I. M.; Nocedal, Jorge; Waltz, Richard A.
21
2004
On the accurate determination of search directions for simple differentiable penalty functions. Zbl 0691.65054
Gould, Nicholas Ian Mark
21
1986
A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. Zbl 1365.65129
Gould, Nicholas I. M.; Scott, Jennifer A.; Hu, Yifan
21
2007
Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares. Zbl 1218.90182
Bellavia, S.; Cartis, C.; Gould, N. I. M.; Morini, B.; Toint, Ph. L.
21
2010
A second derivative SQP method: global convergence. Zbl 1202.49039
Gould, Nicholas I. M.; Robinson, Daniel P.
21
2010
Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. Zbl 1003.65066
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L.
21
2001
On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization. Zbl 1277.68092
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
20
2013
A second derivative SQP method: local convergence and practical issues. Zbl 1202.49040
Gould, Nicholas I. M.; Robinson, Daniel P.
20
2010
Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Phillipe L.
20
2005
On the complexity of finding first-order critical points in constrained nonlinear optimization. Zbl 1301.68154
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
19
2014
Updating the regularization parameter in the adaptive cubic regularization algorithm. Zbl 1259.90134
Gould, N. I. M.; Porcelli, M.; Toint, P. L.
18
2012
Using constraint preconditioners with regularized saddle-point problems. Zbl 1124.65033
Dollar, H. S.; Gould, N. I. M.; Schilders, W. H. A.; Wathen, A. J.
18
2007
Spectral analysis of saddle point matrices with indefinite leading blocks. Zbl 1200.15007
Gould, N. I. M.; Simoncini, V.
17
2010
An exact penalty function for semi-infinite programming. Zbl 0623.90069
Conn, Andrew R.; Gould, Nicholas I. M.
16
1987
On the convergence of successive linear-quadratic programming algorithms. Zbl 1092.90061
Byrd, Richard H.; Gould, Nicholas I. M.; Nocedal, Jorge; Waltz, Richard A.
15
2005
A primal-dual trust-region algorithm for non-convex nonlinear programming. Zbl 0970.90116
Conn, Andrew R.; Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
15
2000
On the convergence of a sequential penalty function method for constrained minimization. Zbl 0667.65050
Gould, Nicholas Ian Mark
15
1989
A filter method with unified step computation for nonlinear optimization. Zbl 1301.49070
Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P.
13
2014
The state-of-the-art of preconditioners for sparse linear least-squares problems. Zbl 1380.65064
Gould, Nicholas; Scott, Jennifer
12
2017
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Zbl 1252.90061
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
12
2012
How good are projection methods for convex feasibility problems? Zbl 1146.90039
Gould, Nicholas I. M.
11
2008
Preconditioning saddle-point systems with applications in optimization. Zbl 1209.65035
Dollar, H. Sue; Gould, Nicholas I. M.; Stoll, Martin; Wathen, Andrew J.
11
2010
On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear constraints and simple bounds. Zbl 0809.65066
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
11
1992
Correction to the paper on global convergence of a class of trust region algorithms for optimization with simple bounds. Zbl 0673.65033
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
11
1989
Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019
Cartis, C.; Gould, N. I. M.; Toint, P. L.
9
2009
An iterative working-set method for large-scale nonconvex quadratic programming. Zbl 1012.65054
Gould, Nicholas I. M.; Toint, Philippe L.
9
2002
An algorithm for large-scale quadratic programming. Zbl 0727.65055
Gould, Nicholas I. M.
8
1991
A weighted Gram-Schmidt method for convex quadratic programming. Zbl 0545.90080
Gill, Philip E.; Gould, Nicholas I. M.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H.
8
1984
On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods. Zbl 1329.65124
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
8
2015
A note on the convergence of barrier algorithms to second-order necessary points. Zbl 0954.90052
Gould, Nicholas I. M.; Toint, Philippe L.
8
1999
A nonmonotone filter SQP method: local convergence and numerical results. Zbl 1326.49042
Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P.
7
2015
Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. Zbl 1339.49023
Curtis, Frank E.; Gould, Nicholas I. M.; Jiang, Hao; Robinson, Daniel P.
7
2016
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. Zbl 1296.90090
Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L.
7
2013
A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. Zbl 1073.65022
Gould, Nicholas I. M.; Scott, Jennifer A.
7
2004
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Zbl 1380.90252
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
7
2017
A second-derivative SQP method with a ‘trust-region-free’ predictor step. Zbl 1246.65089
Gould, Nicholas I. M.; Robinson, Daniel P.
7
2012
Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. Zbl 1428.90160
Gould, Nicholas I. M.; Simoncini, Valeria
7
2020
New crash procedures for large systems of linear constraints. Zbl 0692.90089
Gould, Nicholas I. M.; Reid, John K.
6
1989
Trajectory-following methods for large-scale degenerate convex quadratic programming. Zbl 1272.65051
Gould, Nicholas I. M.; Orban, Dominique; Robinson, Daniel P.
6
2013
On implicit-factorization constraint preconditioners. Zbl 1108.65040
Dollar, H. Sue; Gould, Nicholas I. M.; Wathen, Andrew J.
6
2006
On the location of directions of infinite descent for nonlinear programming algorithms. Zbl 0578.65061
Conn, Andrew R.; Gould, Nicholas I. M.
6
1984
Element-by-element preconditioners for large partially separable optimization problems. Zbl 0897.65045
Daydé, Michel J.; L’Excellent, Jean-Yves; Gould, Nicholas I. M.
6
1997
On modified factorizations for large-scale linearly constrained optimization. Zbl 0957.65063
Gould, Nicholas Ian Mark
6
1999
An interior-point trust-funnel algorithm for nonlinear optimization. Zbl 1355.65075
Curtis, Frank E.; Gould, Nicholas I. M.; Robinson, Daniel P.; Toint, Philippe L.
5
2017
Corrigendum to: “On the complexity of finding first-order critical points in constrained nonlinear optimization”. Zbl 1472.68066
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
5
2017
A dimer-type saddle search algorithm with preconditioning and linesearch. Zbl 1344.65054
Gould, N.; Ortner, C.; Packwood, D.
5
2016
A concise second-order complexity analysis for unconstrained optimization using high-order regularized models. Zbl 1439.90056
Cartis, Coralia; Gould, N. I. M.; Toint, Ph. L.
5
2020
Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints. Zbl 1437.90128
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
5
2020
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Zbl 1012.65046
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L.
5
2002
The multifrontal method in a parallel environment. Zbl 0722.65009
Suff, I. S.; Gould, N. I. M.; Lescrenier, M.; Reid, J. K.
4
1990
SQP methods for large-scale nonlinear programming. Zbl 0970.90050
Gould, Nicholas I. M.
4
2000
On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds. Zbl 0893.90153
Conn, A. R.; Gould, N.; Toint, Ph. L.
4
1997
Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming. Zbl 1130.90399
Gould, Nicholas I. M.; Toint, Philippe L.
4
2006
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization. Zbl 1451.90177
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
4
2018
Erratum to: “Nonlinear programming without a penalty function or a filter”. Zbl 1235.90118
Gould, N. I. M.; Toint, Ph. L.
3
2012
A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints. Zbl 1352.74234
Browne, P. A.; Budd, C.; Gould, N. I. M.; Kim, H. A.; Scott, J. A.
3
2012
Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties. Zbl 1318.90057
Cartis, Coralia; Fowkes, Jaroslav M.; Gould, Nicholas I. M.
3
2015
An introduction to algorithms for nonlinear optimization. Zbl 1027.65083
Gould, Nicholas I. M.; Leyffer, Sven
3
2003
The modified absolute-value factorization norm for trust-region minimization. Zbl 0942.65068
Gould, Nicholas I. M.; Nocedal, Jorge
3
1998
Finding a positive semidefinite interval for a parametric matrix. Zbl 0593.15015
Caron, R. J.; Gould, N. I. M.
3
1986
On solving three classes of nonlinear programming problems via simple differentiable penalty functions. Zbl 0616.90061
Gould, N. I. M.
3
1988
Methods for nonlinear constraints in optimization calculations. Zbl 0881.65056
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
3
1997
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models. Zbl 1425.90113
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
3
2019
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization. Zbl 1415.90118
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
3
2019
Use of the \(P^ 4\) and \(P^ 5\) algorithms for in-core factorization of sparse matrices. Zbl 0711.65015
Arioli, M.; Duff, I. S.; Gould, N. I. M.; Reid, J. K.
2
1990
A note about the complexity of minimizing Nesterov’s smooth Chebyshev-Rosenbrock function. Zbl 1273.90199
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
2
2013
A dual gradient-projection method for large-scale strictly convex quadratic problems. Zbl 1401.90142
Gould, Nicholas I. M.; Robinson, Daniel P.
2
2017
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems. Zbl 1435.90100
Gould, Nicholas I. M.; Rees, Tyrone; Scott, Jennifer A.
2
2019
How good are extrapolated bi-projection methods for linear feasibility problems? Zbl 1244.90157
Gould, Nicholas I. M.
1
2012
A linesearch algorithm with memory for unconstrained optimization. Zbl 0942.65067
Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L.
1
1998
Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. Zbl 1428.90160
Gould, Nicholas I. M.; Simoncini, Valeria
7
2020
A concise second-order complexity analysis for unconstrained optimization using high-order regularized models. Zbl 1439.90056
Cartis, Coralia; Gould, N. I. M.; Toint, Ph. L.
5
2020
Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints. Zbl 1437.90128
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
5
2020
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models. Zbl 1425.90113
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
3
2019
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization. Zbl 1415.90118
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
3
2019
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems. Zbl 1435.90100
Gould, Nicholas I. M.; Rees, Tyrone; Scott, Jennifer A.
2
2019
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization. Zbl 1451.90177
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
4
2018
The state-of-the-art of preconditioners for sparse linear least-squares problems. Zbl 1380.65064
Gould, Nicholas; Scott, Jennifer
12
2017
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Zbl 1380.90252
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
7
2017
An interior-point trust-funnel algorithm for nonlinear optimization. Zbl 1355.65075
Curtis, Frank E.; Gould, Nicholas I. M.; Robinson, Daniel P.; Toint, Philippe L.
5
2017
Corrigendum to: “On the complexity of finding first-order critical points in constrained nonlinear optimization”. Zbl 1472.68066
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
5
2017
A dual gradient-projection method for large-scale strictly convex quadratic problems. Zbl 1401.90142
Gould, Nicholas I. M.; Robinson, Daniel P.
2
2017
A note on performance profiles for benchmarking software. Zbl 1369.65202
Gould, Nicholas; Scott, Jennifer
29
2016
Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. Zbl 1339.49023
Curtis, Frank E.; Gould, Nicholas I. M.; Jiang, Hao; Robinson, Daniel P.
7
2016
A dimer-type saddle search algorithm with preconditioning and linesearch. Zbl 1344.65054
Gould, N.; Ortner, C.; Packwood, D.
5
2016
CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Zbl 1325.90004
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
128
2015
On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods. Zbl 1329.65124
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
8
2015
A nonmonotone filter SQP method: local convergence and numerical results. Zbl 1326.49042
Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P.
7
2015
Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties. Zbl 1318.90057
Cartis, Coralia; Fowkes, Jaroslav M.; Gould, Nicholas I. M.
3
2015
On the complexity of finding first-order critical points in constrained nonlinear optimization. Zbl 1301.68154
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
19
2014
A filter method with unified step computation for nonlinear optimization. Zbl 1301.49070
Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P.
13
2014
On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization. Zbl 1277.68092
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
20
2013
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. Zbl 1296.90090
Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L.
7
2013
Trajectory-following methods for large-scale degenerate convex quadratic programming. Zbl 1272.65051
Gould, Nicholas I. M.; Orban, Dominique; Robinson, Daniel P.
6
2013
A note about the complexity of minimizing Nesterov’s smooth Chebyshev-Rosenbrock function. Zbl 1273.90199
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
2
2013
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity. Zbl 1267.65061
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
33
2012
Complexity bounds for second-order optimality in unconstrained optimization. Zbl 1245.65063
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
28
2012
On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization. Zbl 1250.90083
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
22
2012
Updating the regularization parameter in the adaptive cubic regularization algorithm. Zbl 1259.90134
Gould, N. I. M.; Porcelli, M.; Toint, P. L.
18
2012
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Zbl 1252.90061
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
12
2012
A second-derivative SQP method with a ‘trust-region-free’ predictor step. Zbl 1246.65089
Gould, Nicholas I. M.; Robinson, Daniel P.
7
2012
Erratum to: “Nonlinear programming without a penalty function or a filter”. Zbl 1235.90118
Gould, N. I. M.; Toint, Ph. L.
3
2012
A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints. Zbl 1352.74234
Browne, P. A.; Budd, C.; Gould, N. I. M.; Kim, H. A.; Scott, J. A.
3
2012
How good are extrapolated bi-projection methods for linear feasibility problems? Zbl 1244.90157
Gould, Nicholas I. M.
1
2012
Adaptive cubic regularisation methods for unconstrained optimization. I: Motivation, convergence and numerical results. Zbl 1229.90192
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
111
2011
Adaptive cubic regularisation methods for unconstrained optimization. II: Worst-case function- and derivative-evaluation complexity. Zbl 1229.90193
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
105
2011
On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. Zbl 1236.90118
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L.
38
2011
On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. Zbl 1211.90225
Cartis, C.; Gould, N. I. M.; Toint, Ph. L.
79
2010
Nonlinear programming without a penalty function or a filter. Zbl 1216.90069
Gould, N. I. M.; Toint, Ph. L.
42
2010
On solving trust-region and other regularised subproblems in optimization. Zbl 1193.65098
Gould, Nicholas I. M.; Robinson, Daniel P.; Thorne, H. Sue
36
2010
Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares. Zbl 1218.90182
Bellavia, S.; Cartis, C.; Gould, N. I. M.; Morini, B.; Toint, Ph. L.
21
2010
A second derivative SQP method: global convergence. Zbl 1202.49039
Gould, Nicholas I. M.; Robinson, Daniel P.
21
2010
A second derivative SQP method: local convergence and practical issues. Zbl 1202.49040
Gould, Nicholas I. M.; Robinson, Daniel P.
20
2010
Spectral analysis of saddle point matrices with indefinite leading blocks. Zbl 1200.15007
Gould, N. I. M.; Simoncini, V.
17
2010
Preconditioning saddle-point systems with applications in optimization. Zbl 1209.65035
Dollar, H. Sue; Gould, Nicholas I. M.; Stoll, Martin; Wathen, Andrew J.
11
2010
Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019
Cartis, C.; Gould, N. I. M.; Toint, P. L.
9
2009
How good are projection methods for convex feasibility problems? Zbl 1146.90039
Gould, Nicholas I. M.
11
2008
A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. Zbl 1365.65129
Gould, Nicholas I. M.; Scott, Jennifer A.; Hu, Yifan
21
2007
Using constraint preconditioners with regularized saddle-point problems. Zbl 1124.65033
Dollar, H. S.; Gould, N. I. M.; Schilders, W. H. A.; Wathen, A. J.
18
2007
Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems. Zbl 1104.65310
Dollar, H. Sue; Gould, Nicholas I. M.; Schilders, Wil H. A.; Wathen, Andrew J.
22
2006
On implicit-factorization constraint preconditioners. Zbl 1108.65040
Dollar, H. Sue; Gould, Nicholas I. M.; Wathen, Andrew J.
6
2006
Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming. Zbl 1130.90399
Gould, Nicholas I. M.; Toint, Philippe L.
4
2006
Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Phillipe L.
20
2005
On the convergence of successive linear-quadratic programming algorithms. Zbl 1092.90061
Byrd, Richard H.; Gould, Nicholas I. M.; Nocedal, Jorge; Waltz, Richard A.
15
2005
A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. Zbl 1075.65075
Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.
47
2004
An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Zbl 1146.90513
Byrd, Richard H.; Gould, Nicholas I. M.; Nocedal, Jorge; Waltz, Richard A.
21
2004
A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations. Zbl 1073.65022
Gould, Nicholas I. M.; Scott, Jennifer A.
7
2004
CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. Zbl 1068.90526
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
268
2003
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. Zbl 1068.90525
Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
66
2003
An introduction to algorithms for nonlinear optimization. Zbl 1027.65083
Gould, Nicholas I. M.; Leyffer, Sven
3
2003
Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. Zbl 1038.90076
Fletcher, Roger; Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.; Wächter, Andreas
118
2002
An iterative working-set method for large-scale nonconvex quadratic programming. Zbl 1012.65054
Gould, Nicholas I. M.; Toint, Philippe L.
9
2002
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Zbl 1012.65046
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L.
5
2002
On the solution of equality constrained quadratic programming problems arising in optimization. Zbl 0999.65050
Gould, Nicholas I. M.; Hribar, Mary E.; Nocedal, Jorge
76
2001
Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. Zbl 1003.65066
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L.
21
2001
Trust-region methods. Zbl 0958.65071
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
567
2000
Constraint preconditioning for indefinite linear systems. Zbl 0960.65052
Keller, Carsten; Gould, Nicholas I. M.; Wathen, Andrew J.
168
2000
Exploiting negative curvature directions in linesearch methods for unconstrained optimization. Zbl 0988.90039
Gould, N. I. M.; Lucidi, S.; Roma, M.; Toint, Ph. L.
28
2000
A primal-dual trust-region algorithm for non-convex nonlinear programming. Zbl 0970.90116
Conn, Andrew R.; Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.
15
2000
SQP methods for large-scale nonlinear programming. Zbl 0970.90050
Gould, Nicholas I. M.
4
2000
A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints. Zbl 1138.90447
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
1
2000
Solving the trust-region subproblem using the Lanczos method. Zbl 1047.90510
Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L.
94
1999
A note on the convergence of barrier algorithms to second-order necessary points. Zbl 0954.90052
Gould, Nicholas I. M.; Toint, Philippe L.
8
1999
On modified factorizations for large-scale linearly constrained optimization. Zbl 0957.65063
Gould, Nicholas Ian Mark
6
1999
Sparse approximate-inverse preconditioners using norm-minimization techniques. Zbl 0911.65037
Gould, Nicholas I. M.; Scott, Jennifer A.
27
1998
The modified absolute-value factorization norm for trust-region minimization. Zbl 0942.65068
Gould, Nicholas I. M.; Nocedal, Jorge
3
1998
A linesearch algorithm with memory for unconstrained optimization. Zbl 0942.65067
Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L.
1
1998
Element-by-element preconditioners for large partially separable optimization problems. Zbl 0897.65045
Daydé, Michel J.; L’Excellent, Jean-Yves; Gould, Nicholas I. M.
6
1997
On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds. Zbl 0893.90153
Conn, A. R.; Gould, N.; Toint, Ph. L.
4
1997
Methods for nonlinear constraints in optimization calculations. Zbl 0881.65056
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
3
1997
Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints. Zbl 0856.90098
Conn, A. R.; Gould, N.; Sartenaer, A.; Toint, Ph. L.
36
1996
CUTE: Constrained and unconstrained testing environment. Zbl 0886.65058
Bongartz, I.; Conn, A. R.; Gould, N.; Toint, Ph. L.
314
1995
On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear constraints and simple bounds. Zbl 0809.65066
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
11
1992
A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. Zbl 0724.65067
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
162
1991
Convergence of quasi-Newton matrices generated by the symmetric rank one update. Zbl 0737.90062
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
56
1991
The factorization of sparse symmetric indefinite matrices. Zbl 0739.65018
Duff, I. S.; Gould, N. I. M.; Reid, J. K.; Scott, J. A.
23
1991
An algorithm for large-scale quadratic programming. Zbl 0727.65055
Gould, Nicholas I. M.
8
1991
The multifrontal method in a parallel environment. Zbl 0722.65009
Suff, I. S.; Gould, N. I. M.; Lescrenier, M.; Reid, J. K.
4
1990
Use of the \(P^ 4\) and \(P^ 5\) algorithms for in-core factorization of sparse matrices. Zbl 0711.65015
Arioli, M.; Duff, I. S.; Gould, N. I. M.; Reid, J. K.
2
1990
On the convergence of a sequential penalty function method for constrained minimization. Zbl 0667.65050
Gould, Nicholas Ian Mark
15
1989
Correction to the paper on global convergence of a class of trust region algorithms for optimization with simple bounds. Zbl 0673.65033
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
11
1989
New crash procedures for large systems of linear constraints. Zbl 0692.90089
Gould, Nicholas I. M.; Reid, John K.
6
1989
Global convergence of a class of trust region algorithms for optimization with simple bounds. Zbl 0643.65031
Conn, A. R.; Gould, N. I. M.; Toint, Ph. L.
99
1988
Testing a class of methods for solving minimization problems with simple bounds on the variables. Zbl 0645.65033
Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.
51
1988
On solving three classes of nonlinear programming problems via simple differentiable penalty functions. Zbl 0616.90061
Gould, N. I. M.
3
1988
An exact penalty function for semi-infinite programming. Zbl 0623.90069
Conn, Andrew R.; Gould, Nicholas I. M.
16
1987
On the accurate determination of search directions for simple differentiable penalty functions. Zbl 0691.65054
Gould, Nicholas Ian Mark
21
1986
Finding a positive semidefinite interval for a parametric matrix. Zbl 0593.15015
Caron, R. J.; Gould, N. I. M.
3
1986
On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. Zbl 0591.90068
Gould, Nicholas I. M.
32
1985
A weighted Gram-Schmidt method for convex quadratic programming. Zbl 0545.90080
Gill, Philip E.; Gould, Nicholas I. M.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H.
8
1984
...and 1 more Documents
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Cited by 2,169 Authors

51 Martínez, José Mario
47 Toint, Philippe L.
39 Babaie-Kafaki, Saman
32 Zhu, Detong
27 Birgin, Ernesto G.
24 Gould, Nicholas Ian Mark
21 Cartis, Coralia
21 Orban, Dominique
21 Robinson, Daniel P.
19 Ma, Changfeng
18 Gratton, Serge
18 Jian, Jinbao
18 Santos, Sandra Augusta
18 Shen, Chungen
18 Vicente, Luis Nunes
17 Curtis, Frank E.
17 Dostál, Zdeněk
17 Yuan, Ya-xiang
17 Zhang, Guofeng
16 Kimiaei, Morteza
16 Pu, Dingguo
14 Audet, Charles
14 Bellavia, Stefania
14 Gu, Chao
14 Sun, Wenyu
13 Fasano, Giovanni
13 Morini, Benedetta
13 Salahi, Maziar
12 Amini, Keyvan
12 Aminifard, Zohre
12 Dai, Yu-Hong
12 Ghanbari, Reza
12 Grapiglia, Geovani Nunes
12 Liang, Zhaozheng
12 Nocedal, Jorge
12 Scott, Jennifer A.
11 Chen, Zhongwen
11 Conn, Andrew Roger
11 Karas, Elizabeth W.
11 Le Digabel, Sébastien
11 Marcia, Roummel F.
11 Yuan, Gonglin
11 Zhang, Lei-Hong
10 Armand, Paul
10 Diehl, Moritz Mathias
10 Kanzow, Christian
10 Liu, Zexian
10 Ni, Qin
10 Peyghami, Mohammad Reza
10 Roma, Massimo
10 Xia, Yong
9 Ahookhosh, Masoud
9 Andreani, Roberto
9 Bergamaschi, Luca
9 Byrd, Richard H.
9 Gondzio, Jacek
9 Huang, Na
9 Porcelli, Margherita
9 Wei, Zengxin
9 Zhang, Liwei
8 Biegler, Lorenz T.
8 di Serafino, Daniela
8 Erway, Jennifer B.
8 Fernandes, Edite M. G. P.
8 Leyffer, Sven
8 Lucidi, Stefano
8 Lukšan, Ladislav
8 Luo, Xinlong
8 Mahdavi-Amiri, Nezam
8 Nesterov, Yurii
8 Royer, Clément W.
8 Su, Ke
8 Tůma, Miroslav
7 De Simone, Valentina
7 Dussault, Jean-Pierre
7 Esmaeili, Hamid
7 Fatemi, Masoud
7 Ferronato, Massimiliano
7 Kamandi, Ahmad
7 Kungurtsev, Vyacheslav
7 Noll, Dominikus
7 Petra, Cosmin G.
7 Qiu, Songqiang
7 Riccietti, Elisa
7 Wächter, Andreas
7 Wang, Changyu
7 Wang, Zhujun
7 Wei, Yimin
7 Xue, Wenjuan
7 Yamashita, Nobuo
7 Yuan, Jinyun
7 Zhang, Hongchao
7 Zhu, Xiaojing
6 Al-Baali, Mehiddin
6 Apkarian, Pierre
6 Brust, Johannes J.
6 Cao, Yang
6 Gould, Nick I. M.
6 Li, Wen
6 Pham Dinh Tao
...and 2,069 more Authors
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Cited in 216 Serials

151 Computational Optimization and Applications
122 Mathematical Programming. Series A. Series B
110 Optimization Methods & Software
84 Journal of Optimization Theory and Applications
81 SIAM Journal on Optimization
72 Applied Mathematics and Computation
68 Journal of Computational and Applied Mathematics
54 Numerical Algorithms
53 Journal of Global Optimization
36 Optimization
32 Optimization Letters
31 Computational and Applied Mathematics
30 Computers & Mathematics with Applications
29 International Journal of Computer Mathematics
28 European Journal of Operational Research
24 Computer Methods in Applied Mechanics and Engineering
24 SIAM Journal on Scientific Computing
24 Mathematical Programming Computation
21 Applied Numerical Mathematics
19 Numerical Linear Algebra with Applications
18 Numerical Functional Analysis and Optimization
18 Linear Algebra and its Applications
18 Optimization and Engineering
18 Journal of Applied Mathematics and Computing
16 Journal of Computational Physics
15 SIAM Journal on Matrix Analysis and Applications
15 Annals of Operations Research
13 BIT
11 Mathematics of Computation
11 International Journal for Numerical Methods in Engineering
11 Applied Mathematical Modelling
10 Mathematical Problems in Engineering
10 Abstract and Applied Analysis
10 Mathematical Methods of Operations Research
10 Journal of Industrial and Management Optimization
9 Applied Mathematics and Optimization
8 Calcolo
8 Asia-Pacific Journal of Operational Research
8 Journal of Scientific Computing
8 Computational Geosciences
8 Journal of Systems Science and Complexity
8 Journal of Applied Mathematics
8 Science China. Mathematics
8 Numerical Algebra, Control and Optimization
8 Journal of the Operations Research Society of China
7 Operations Research Letters
7 Journal of Inequalities and Applications
6 Computing
6 Mathematics of Operations Research
6 Numerische Mathematik
6 Computers & Operations Research
6 SIAM Review
6 4OR
6 East Asian Journal on Applied Mathematics
5 Engineering Optimization
4 Inverse Problems
4 ACM Transactions on Mathematical Software
4 Automatica
4 SIAM Journal on Numerical Analysis
4 Mathematical and Computer Modelling
4 INFORMS Journal on Computing
4 Discrete Dynamics in Nature and Society
4 Acta Mathematica Sinica. English Series
4 RAIRO. Operations Research
4 Structural and Multidisciplinary Optimization
4 Journal of Mathematical Modeling
3 International Journal for Numerical Methods in Fluids
3 SIAM Journal on Control and Optimization
3 Acta Mathematicae Applicatae Sinica. English Series
3 Journal of Complexity
3 Applied Mathematics Letters
3 Science in China. Series A
3 Applications of Mathematics
3 Computational Statistics and Data Analysis
3 International Journal of Robust and Nonlinear Control
3 Top
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 International Journal of Applied Mathematics and Computer Science
3 Acta Numerica
3 Statistics and Computing
3 S\(\vec{\text{e}}\)MA Journal
3 EURO Journal on Computational Optimization
3 SN Operations Research Forum
2 International Journal of Control
2 International Journal for Numerical and Analytical Methods in Geomechanics
2 Journal of Mathematical Analysis and Applications
2 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
2 Kybernetika
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Optimal Control Applications & Methods
2 Applied Mathematics and Mechanics. (English Edition)
2 Acta Applicandae Mathematicae
2 Bulletin of the Iranian Mathematical Society
2 Computational Mechanics
2 Neural Computation
2 Japan Journal of Industrial and Applied Mathematics
2 Automation and Remote Control
2 Journal of Mathematical Imaging and Vision
2 Journal of Nonlinear Science
2 Applied Mathematics. Series B (English Edition)
...and 116 more Serials
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Cited in 44 Fields

1,297 Operations research, mathematical programming (90-XX)
944 Numerical analysis (65-XX)
289 Calculus of variations and optimal control; optimization (49-XX)
81 Computer science (68-XX)
59 Fluid mechanics (76-XX)
58 Mechanics of deformable solids (74-XX)
52 Linear and multilinear algebra; matrix theory (15-XX)
46 Partial differential equations (35-XX)
44 Systems theory; control (93-XX)
30 Statistics (62-XX)
24 Information and communication theory, circuits (94-XX)
19 Biology and other natural sciences (92-XX)
12 Ordinary differential equations (34-XX)
12 Global analysis, analysis on manifolds (58-XX)
10 Geophysics (86-XX)
9 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Operator theory (47-XX)
8 Probability theory and stochastic processes (60-XX)
8 Optics, electromagnetic theory (78-XX)
7 Approximations and expansions (41-XX)
7 Quantum theory (81-XX)
6 Statistical mechanics, structure of matter (82-XX)
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3 Combinatorics (05-XX)
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2 Nonassociative rings and algebras (17-XX)
2 Difference and functional equations (39-XX)
1 General and overarching topics; collections (00-XX)
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1 Functions of a complex variable (30-XX)
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1 Convex and discrete geometry (52-XX)
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