Edit Profile (opens in new tab) Gould, Nicholas Ian Mark Compute Distance To: Compute Author ID: gould.nicholas-ian-mark Published as: Gould, Nicholas I. M.; Gould, Nicholas Ian Mark; Gould, N. I. M.; Gould, Nicholas more...less Documents Indexed: 106 Publications since 1984, including 2 Books Co-Authors: 42 Co-Authors with 94 Joint Publications 1,076 Co-Co-Authors all top 5 Co-Authors 10 single-authored 54 Toint, Philippe L. 24 Cartis, Coralia 16 Conn, Andrew Roger 10 Robinson, Daniel P. 8 Orban, Dominique 8 Scott, Jennifer A. 5 Wathen, Andrew John 4 Dollar, H. Sue 4 Nocedal, Jorge 4 Reid, John 4 Sartenaer, Annick 3 Leyffer, Sven 3 Lucidi, Stefano 3 Roma, Massimo 2 Byrd, Richard H. 2 Curtis, Frank E. 2 Daydé, Michel J. 2 Duff, Iain S. 2 Fowkes, Jaroslav M. 2 Loh, Yueling 2 Schilders, Wil H. A. 2 Simoncini, Valeria 2 Waltz, Richard A. 1 Arioli, Mario 1 Bellavia, Stefania 1 Bongartz, Ingrid 1 Browne, Philip A. 1 Budd, Christopher John 1 Caron, Richard J. 1 Décamps, Jérôme P. 1 Farmer, Chris L. 1 Fletcher, Roger 1 Gill, Philip E. 1 Hribar, Mary E. 1 Hu, Yifan 1 Jiang, Hao 1 Keller, Carsten 1 Kim, H. Alicia 1 Lange, Marius 1 Lescrenier, Marc J. A. 1 L’Excellent, Jean-Yves 1 Morini, Benedetta 1 Murray, Walter 1 Ortner, Christoph 1 Porcelli, Margherita 1 Rees, Tyrone 1 Saunders, Michael A. 1 Stoll, Martin 1 Suff, I. S. 1 Thorne, H. Sue 1 Wächter, Andreas 1 Wright, Margaret H. all top 5 Serials 16 SIAM Journal on Optimization 13 Mathematical Programming. Series A. Series B 8 Computational Optimization and Applications 7 ACM Transactions on Mathematical Software 7 SIAM Journal on Numerical Analysis 7 Optimization Methods & Software 5 IMA Journal of Numerical Analysis 4 SIAM Journal on Scientific Computing 3 Mathematical Programming 3 SIAM Journal on Matrix Analysis and Applications 2 Mathematics of Computation 2 BIT 2 Journal of Complexity 2 Journal of Global Optimization 2 Mathematical Programming Computation 1 International Journal for Numerical Methods in Engineering 1 Journal of Optimization Theory and Applications 1 SIAM Journal on Scientific and Statistical Computing 1 Applied Numerical Mathematics 1 Linear Algebra and its Applications 1 Numerical Linear Algebra with Applications 1 4OR 1 MPS/SIAM Series on Optimization all top 5 Fields 92 Operations research, mathematical programming (90-XX) 78 Numerical analysis (65-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 10 Computer science (68-XX) 4 Global analysis, analysis on manifolds (58-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 2,679 times in 1,723 Documents Cited by ▼ Year ▼ Trust-region methods. Zbl 0958.65071Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 567 2000 CUTE: Constrained and unconstrained testing environment. Zbl 0886.65058Bongartz, I.; Conn, A. R.; Gould, N.; Toint, Ph. L. 314 1995 CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. Zbl 1068.90526Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 268 2003 Constraint preconditioning for indefinite linear systems. Zbl 0960.65052Keller, 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 0724.65067Conn, 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 1325.90004Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 128 2015 Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. Zbl 1038.90076Fletcher, 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 1229.90192Cartis, 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 1229.90193Cartis, 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 0643.65031Conn, A. R.; Gould, N. I. M.; Toint, Ph. L. 99 1988 Solving the trust-region subproblem using the Lanczos method. Zbl 1047.90510Gould, 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 1211.90225Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 79 2010 On the solution of equality constrained quadratic programming problems arising in optimization. Zbl 0999.65050Gould, 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 1068.90525Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 66 2003 Convergence of quasi-Newton matrices generated by the symmetric rank one update. Zbl 0737.90062Conn, 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 0645.65033Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 51 1988 A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. Zbl 1075.65075Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L. 47 2004 Nonlinear programming without a penalty function or a filter. Zbl 1216.90069Gould, N. I. M.; Toint, Ph. L. 42 2010 On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. Zbl 1236.90118Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 38 2011 On solving trust-region and other regularised subproblems in optimization. Zbl 1193.65098Gould, 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 0856.90098Conn, 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 1267.65061Cartis, 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 0591.90068Gould, Nicholas I. M. 32 1985 A note on performance profiles for benchmarking software. Zbl 1369.65202Gould, Nicholas; Scott, Jennifer 29 2016 Complexity bounds for second-order optimality in unconstrained optimization. Zbl 1245.65063Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 28 2012 Exploiting negative curvature directions in linesearch methods for unconstrained optimization. Zbl 0988.90039Gould, N. I. M.; Lucidi, S.; Roma, M.; Toint, Ph. L. 28 2000 Sparse approximate-inverse preconditioners using norm-minimization techniques. Zbl 0911.65037Gould, Nicholas I. M.; Scott, Jennifer A. 27 1998 The factorization of sparse symmetric indefinite matrices. Zbl 0739.65018Duff, 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 1250.90083Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 22 2012 Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems. Zbl 1104.65310Dollar, 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 1146.90513Byrd, 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 0691.65054Gould, Nicholas Ian Mark 21 1986 A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. Zbl 1365.65129Gould, Nicholas I. M.; Scott, Jennifer A.; Hu, Yifan 21 2007 Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares. Zbl 1218.90182Bellavia, S.; Cartis, C.; Gould, N. I. M.; Morini, B.; Toint, Ph. L. 21 2010 A second derivative SQP method: global convergence. Zbl 1202.49039Gould, Nicholas I. M.; Robinson, Daniel P. 21 2010 Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. Zbl 1003.65066Gould, 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 1277.68092Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 20 2013 A second derivative SQP method: local convergence and practical issues. Zbl 1202.49040Gould, Nicholas I. M.; Robinson, Daniel P. 20 2010 Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060Gould, 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 1301.68154Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 19 2014 Updating the regularization parameter in the adaptive cubic regularization algorithm. Zbl 1259.90134Gould, N. I. M.; Porcelli, M.; Toint, P. L. 18 2012 Using constraint preconditioners with regularized saddle-point problems. Zbl 1124.65033Dollar, 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 1200.15007Gould, N. I. M.; Simoncini, V. 17 2010 An exact penalty function for semi-infinite programming. Zbl 0623.90069Conn, Andrew R.; Gould, Nicholas I. M. 16 1987 On the convergence of successive linear-quadratic programming algorithms. Zbl 1092.90061Byrd, 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 0970.90116Conn, 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 0667.65050Gould, Nicholas Ian Mark 15 1989 A filter method with unified step computation for nonlinear optimization. Zbl 1301.49070Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P. 13 2014 The state-of-the-art of preconditioners for sparse linear least-squares problems. Zbl 1380.65064Gould, Nicholas; Scott, Jennifer 12 2017 Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Zbl 1252.90061Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 12 2012 How good are projection methods for convex feasibility problems? Zbl 1146.90039Gould, Nicholas I. M. 11 2008 Preconditioning saddle-point systems with applications in optimization. Zbl 1209.65035Dollar, 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 0809.65066Conn, 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 0673.65033Conn, A. R.; Gould, N. I. M.; Toint, Ph. L. 11 1989 Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019Cartis, C.; Gould, N. I. M.; Toint, P. L. 9 2009 An iterative working-set method for large-scale nonconvex quadratic programming. Zbl 1012.65054Gould, Nicholas I. M.; Toint, Philippe L. 9 2002 An algorithm for large-scale quadratic programming. Zbl 0727.65055Gould, Nicholas I. M. 8 1991 A weighted Gram-Schmidt method for convex quadratic programming. Zbl 0545.90080Gill, 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 1329.65124Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 8 2015 A note on the convergence of barrier algorithms to second-order necessary points. Zbl 0954.90052Gould, Nicholas I. M.; Toint, Philippe L. 8 1999 A nonmonotone filter SQP method: local convergence and numerical results. Zbl 1326.49042Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P. 7 2015 Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. Zbl 1339.49023Curtis, 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 1296.90090Fowkes, 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 1073.65022Gould, Nicholas I. M.; Scott, Jennifer A. 7 2004 Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Zbl 1380.90252Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 7 2017 A second-derivative SQP method with a ‘trust-region-free’ predictor step. Zbl 1246.65089Gould, Nicholas I. M.; Robinson, Daniel P. 7 2012 Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. Zbl 1428.90160Gould, Nicholas I. M.; Simoncini, Valeria 7 2020 New crash procedures for large systems of linear constraints. Zbl 0692.90089Gould, Nicholas I. M.; Reid, John K. 6 1989 Trajectory-following methods for large-scale degenerate convex quadratic programming. Zbl 1272.65051Gould, Nicholas I. M.; Orban, Dominique; Robinson, Daniel P. 6 2013 On implicit-factorization constraint preconditioners. Zbl 1108.65040Dollar, H. Sue; Gould, Nicholas I. M.; Wathen, Andrew J. 6 2006 On the location of directions of infinite descent for nonlinear programming algorithms. Zbl 0578.65061Conn, Andrew R.; Gould, Nicholas I. M. 6 1984 Element-by-element preconditioners for large partially separable optimization problems. Zbl 0897.65045Daydé, Michel J.; L’Excellent, Jean-Yves; Gould, Nicholas I. M. 6 1997 On modified factorizations for large-scale linearly constrained optimization. Zbl 0957.65063Gould, Nicholas Ian Mark 6 1999 An interior-point trust-funnel algorithm for nonlinear optimization. Zbl 1355.65075Curtis, 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 1472.68066Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 5 2017 A dimer-type saddle search algorithm with preconditioning and linesearch. Zbl 1344.65054Gould, N.; Ortner, C.; Packwood, D. 5 2016 A concise second-order complexity analysis for unconstrained optimization using high-order regularized models. Zbl 1439.90056Cartis, 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 1437.90128Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 5 2020 Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Zbl 1012.65046Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L. 5 2002 The multifrontal method in a parallel environment. Zbl 0722.65009Suff, I. S.; Gould, N. I. M.; Lescrenier, M.; Reid, J. K. 4 1990 SQP methods for large-scale nonlinear programming. Zbl 0970.90050Gould, 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 0893.90153Conn, A. R.; Gould, N.; Toint, Ph. L. 4 1997 Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming. Zbl 1130.90399Gould, Nicholas I. M.; Toint, Philippe L. 4 2006 Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization. Zbl 1451.90177Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 4 2018 Erratum to: “Nonlinear programming without a penalty function or a filter”. Zbl 1235.90118Gould, 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 1352.74234Browne, 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 1318.90057Cartis, Coralia; Fowkes, Jaroslav M.; Gould, Nicholas I. M. 3 2015 An introduction to algorithms for nonlinear optimization. Zbl 1027.65083Gould, Nicholas I. M.; Leyffer, Sven 3 2003 The modified absolute-value factorization norm for trust-region minimization. Zbl 0942.65068Gould, Nicholas I. M.; Nocedal, Jorge 3 1998 Finding a positive semidefinite interval for a parametric matrix. Zbl 0593.15015Caron, R. J.; Gould, N. I. M. 3 1986 On solving three classes of nonlinear programming problems via simple differentiable penalty functions. Zbl 0616.90061Gould, N. I. M. 3 1988 Methods for nonlinear constraints in optimization calculations. Zbl 0881.65056Conn, 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 1425.90113Cartis, 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 1415.90118Cartis, 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 0711.65015Arioli, 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 1273.90199Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 2 2013 A dual gradient-projection method for large-scale strictly convex quadratic problems. Zbl 1401.90142Gould, 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 1435.90100Gould, Nicholas I. M.; Rees, Tyrone; Scott, Jennifer A. 2 2019 How good are extrapolated bi-projection methods for linear feasibility problems? Zbl 1244.90157Gould, Nicholas I. M. 1 2012 A linesearch algorithm with memory for unconstrained optimization. Zbl 0942.65067Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L. 1 1998 Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. Zbl 1428.90160Gould, Nicholas I. M.; Simoncini, Valeria 7 2020 A concise second-order complexity analysis for unconstrained optimization using high-order regularized models. Zbl 1439.90056Cartis, 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 1437.90128Cartis, 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 1425.90113Cartis, 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 1415.90118Cartis, 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 1435.90100Gould, 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 1451.90177Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 4 2018 The state-of-the-art of preconditioners for sparse linear least-squares problems. Zbl 1380.65064Gould, Nicholas; Scott, Jennifer 12 2017 Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Zbl 1380.90252Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 7 2017 An interior-point trust-funnel algorithm for nonlinear optimization. Zbl 1355.65075Curtis, 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 1472.68066Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 5 2017 A dual gradient-projection method for large-scale strictly convex quadratic problems. Zbl 1401.90142Gould, Nicholas I. M.; Robinson, Daniel P. 2 2017 A note on performance profiles for benchmarking software. Zbl 1369.65202Gould, Nicholas; Scott, Jennifer 29 2016 Adaptive augmented Lagrangian methods: algorithms and practical numerical experience. Zbl 1339.49023Curtis, Frank E.; Gould, Nicholas I. M.; Jiang, Hao; Robinson, Daniel P. 7 2016 A dimer-type saddle search algorithm with preconditioning and linesearch. Zbl 1344.65054Gould, N.; Ortner, C.; Packwood, D. 5 2016 CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Zbl 1325.90004Gould, 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 1329.65124Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 8 2015 A nonmonotone filter SQP method: local convergence and numerical results. Zbl 1326.49042Gould, Nicholas I. M.; Loh, Yueling; Robinson, Daniel P. 7 2015 Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties. Zbl 1318.90057Cartis, Coralia; Fowkes, Jaroslav M.; Gould, Nicholas I. M. 3 2015 On the complexity of finding first-order critical points in constrained nonlinear optimization. Zbl 1301.68154Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 19 2014 A filter method with unified step computation for nonlinear optimization. Zbl 1301.49070Gould, 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 1277.68092Cartis, 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 1296.90090Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L. 7 2013 Trajectory-following methods for large-scale degenerate convex quadratic programming. Zbl 1272.65051Gould, Nicholas I. M.; Orban, Dominique; Robinson, Daniel P. 6 2013 A note about the complexity of minimizing Nesterov’s smooth Chebyshev-Rosenbrock function. Zbl 1273.90199Cartis, 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 1267.65061Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 33 2012 Complexity bounds for second-order optimality in unconstrained optimization. Zbl 1245.65063Cartis, 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 1250.90083Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 22 2012 Updating the regularization parameter in the adaptive cubic regularization algorithm. Zbl 1259.90134Gould, N. I. M.; Porcelli, M.; Toint, P. L. 18 2012 Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Zbl 1252.90061Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 12 2012 A second-derivative SQP method with a ‘trust-region-free’ predictor step. Zbl 1246.65089Gould, Nicholas I. M.; Robinson, Daniel P. 7 2012 Erratum to: “Nonlinear programming without a penalty function or a filter”. Zbl 1235.90118Gould, 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 1352.74234Browne, 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 1244.90157Gould, Nicholas I. M. 1 2012 Adaptive cubic regularisation methods for unconstrained optimization. I: Motivation, convergence and numerical results. Zbl 1229.90192Cartis, 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 1229.90193Cartis, 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 1236.90118Cartis, 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 1211.90225Cartis, C.; Gould, N. I. M.; Toint, Ph. L. 79 2010 Nonlinear programming without a penalty function or a filter. Zbl 1216.90069Gould, N. I. M.; Toint, Ph. L. 42 2010 On solving trust-region and other regularised subproblems in optimization. Zbl 1193.65098Gould, Nicholas I. M.; Robinson, Daniel P.; Thorne, H. Sue 36 2010 Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares. Zbl 1218.90182Bellavia, S.; Cartis, C.; Gould, N. I. M.; Morini, B.; Toint, Ph. L. 21 2010 A second derivative SQP method: global convergence. Zbl 1202.49039Gould, Nicholas I. M.; Robinson, Daniel P. 21 2010 A second derivative SQP method: local convergence and practical issues. Zbl 1202.49040Gould, Nicholas I. M.; Robinson, Daniel P. 20 2010 Spectral analysis of saddle point matrices with indefinite leading blocks. Zbl 1200.15007Gould, N. I. M.; Simoncini, V. 17 2010 Preconditioning saddle-point systems with applications in optimization. Zbl 1209.65035Dollar, H. Sue; Gould, Nicholas I. M.; Stoll, Martin; Wathen, Andrew J. 11 2010 Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019Cartis, C.; Gould, N. I. M.; Toint, P. L. 9 2009 How good are projection methods for convex feasibility problems? Zbl 1146.90039Gould, Nicholas I. M. 11 2008 A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. Zbl 1365.65129Gould, Nicholas I. M.; Scott, Jennifer A.; Hu, Yifan 21 2007 Using constraint preconditioners with regularized saddle-point problems. Zbl 1124.65033Dollar, 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 1104.65310Dollar, H. Sue; Gould, Nicholas I. M.; Schilders, Wil H. A.; Wathen, Andrew J. 22 2006 On implicit-factorization constraint preconditioners. Zbl 1108.65040Dollar, 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 1130.90399Gould, Nicholas I. M.; Toint, Philippe L. 4 2006 Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Phillipe L. 20 2005 On the convergence of successive linear-quadratic programming algorithms. Zbl 1092.90061Byrd, 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 1075.65075Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L. 47 2004 An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Zbl 1146.90513Byrd, 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 1073.65022Gould, Nicholas I. M.; Scott, Jennifer A. 7 2004 CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. Zbl 1068.90526Gould, 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 1068.90525Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 66 2003 An introduction to algorithms for nonlinear optimization. Zbl 1027.65083Gould, Nicholas I. M.; Leyffer, Sven 3 2003 Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. Zbl 1038.90076Fletcher, 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 1012.65054Gould, Nicholas I. M.; Toint, Philippe L. 9 2002 Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Zbl 1012.65046Gould, 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 0999.65050Gould, Nicholas I. M.; Hribar, Mary E.; Nocedal, Jorge 76 2001 Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. Zbl 1003.65066Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L. 21 2001 Trust-region methods. Zbl 0958.65071Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 567 2000 Constraint preconditioning for indefinite linear systems. Zbl 0960.65052Keller, Carsten; Gould, Nicholas I. M.; Wathen, Andrew J. 168 2000 Exploiting negative curvature directions in linesearch methods for unconstrained optimization. Zbl 0988.90039Gould, N. I. M.; Lucidi, S.; Roma, M.; Toint, Ph. L. 28 2000 A primal-dual trust-region algorithm for non-convex nonlinear programming. Zbl 0970.90116Conn, Andrew R.; Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 15 2000 SQP methods for large-scale nonlinear programming. Zbl 0970.90050Gould, Nicholas I. M. 4 2000 A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints. Zbl 1138.90447Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 1 2000 Solving the trust-region subproblem using the Lanczos method. Zbl 1047.90510Gould, 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 0954.90052Gould, Nicholas I. M.; Toint, Philippe L. 8 1999 On modified factorizations for large-scale linearly constrained optimization. Zbl 0957.65063Gould, Nicholas Ian Mark 6 1999 Sparse approximate-inverse preconditioners using norm-minimization techniques. Zbl 0911.65037Gould, Nicholas I. M.; Scott, Jennifer A. 27 1998 The modified absolute-value factorization norm for trust-region minimization. Zbl 0942.65068Gould, Nicholas I. M.; Nocedal, Jorge 3 1998 A linesearch algorithm with memory for unconstrained optimization. Zbl 0942.65067Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L. 1 1998 Element-by-element preconditioners for large partially separable optimization problems. Zbl 0897.65045Daydé, 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 0893.90153Conn, A. R.; Gould, N.; Toint, Ph. L. 4 1997 Methods for nonlinear constraints in optimization calculations. Zbl 0881.65056Conn, 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 0856.90098Conn, A. R.; Gould, N.; Sartenaer, A.; Toint, Ph. L. 36 1996 CUTE: Constrained and unconstrained testing environment. Zbl 0886.65058Bongartz, 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 0809.65066Conn, 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 0724.65067Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 162 1991 Convergence of quasi-Newton matrices generated by the symmetric rank one update. Zbl 0737.90062Conn, A. R.; Gould, N. I. M.; Toint, Ph. L. 56 1991 The factorization of sparse symmetric indefinite matrices. Zbl 0739.65018Duff, I. S.; Gould, N. I. M.; Reid, J. K.; Scott, J. A. 23 1991 An algorithm for large-scale quadratic programming. Zbl 0727.65055Gould, Nicholas I. M. 8 1991 The multifrontal method in a parallel environment. Zbl 0722.65009Suff, 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 0711.65015Arioli, 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 0667.65050Gould, 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 0673.65033Conn, A. R.; Gould, N. I. M.; Toint, Ph. L. 11 1989 New crash procedures for large systems of linear constraints. Zbl 0692.90089Gould, Nicholas I. M.; Reid, John K. 6 1989 Global convergence of a class of trust region algorithms for optimization with simple bounds. Zbl 0643.65031Conn, 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 0645.65033Conn, 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 0616.90061Gould, N. I. M. 3 1988 An exact penalty function for semi-infinite programming. Zbl 0623.90069Conn, Andrew R.; Gould, Nicholas I. M. 16 1987 On the accurate determination of search directions for simple differentiable penalty functions. Zbl 0691.65054Gould, Nicholas Ian Mark 21 1986 Finding a positive semidefinite interval for a parametric matrix. Zbl 0593.15015Caron, 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 0591.90068Gould, Nicholas I. M. 32 1985 A weighted Gram-Schmidt method for convex quadratic programming. Zbl 0545.90080Gill, Philip E.; Gould, Nicholas I. M.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H. 8 1984 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 Cited in 216 Serials 151 Computational Optimization and Applications 122 Mathematical Programming. Series A. 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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. 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Series B (English Edition) ...and 116 more Serials all top 5 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) 5 History and biography (01-XX) 5 Real functions (26-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of particles and systems (70-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Combinatorics (05-XX) 3 Functional analysis (46-XX) 3 Differential geometry (53-XX) 2 Nonassociative rings and algebras (17-XX) 2 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) Citations by Year