Edit Profile (opens in new tab) Toint, Philippe L. Compute Distance To: Compute Author ID: toint.philippe-l Published as: Toint, Philippe L.; Toint, Ph. L.; Toint, Philippe; Toint, P. L.; Toint, Ph.; Toint, Phillipe L.; Toint, P. more...less Homepage: http://perso.fundp.ac.be/~phtoint/toint.html External Links: MGP · ORCID · dblp Documents Indexed: 171 Publications since 1977, including 3 Books 2 Contributions as Editor · 1 Further Contribution Co-Authors: 68 Co-Authors with 150 Joint Publications 1,600 Co-Co-Authors all top 5 Co-Authors 17 single-authored 33 Gould, Nicholas Ian Mark 31 Conn, Andrew Roger 26 Cartis, Coralia 22 Gould, Nick I. M. 19 Gratton, Serge 10 Sartenaer, Annick 9 Orban, Dominique 6 Griewank, Andreas 5 Porcelli, Margherita 4 Bastin, Fabian 4 Callier, Frank M. 4 Cirillo, Cinzia 4 Leyffer, Sven 4 Malmedy, Vincent 4 Morini, Benedetta 4 Mouffe, Mélodie 4 Simon, Ehouarn 3 Bellavia, Stefania 3 Lucidi, Stefano 3 Roma, Massimo 3 Sampaio, Phillipe R. 3 Scheinberg, Katya 3 Titley-Péloquin, David 3 Tomanos, Dimitri 3 Tuyttens, Daniel 2 Bierlaire, Michel 2 Birgin, Ernesto G. 2 Colson, Benoît 2 Fares, M’Barek 2 Fletcher, Roger 2 Gardenghi, J. L. 2 Gurioli, Gianmarco 2 Manneback, P. E. 2 Martínez, José Mario 2 Powell, Michael James David 2 Sainvitu, Caroline 2 Santos, Sandra Augusta 2 Viloche Bazán, Fermín S. 2 Weber-Mendonça, Melissa 2 Yuan, Ya-xiang 1 Al-Baali, Mehiddin 1 Blewitt, R. A. 1 Bongartz, Ingrid 1 Campbell, L. H. 1 Cornelis, Eric 1 Curtis, Frank E. 1 De Zeeuw, Aart J. 1 Gay, David M. 1 Germain, Marc 1 Goldfarb, Donald 1 Golub, Gene Howard 1 Gürol, Selime 1 Ilunga, Jean Tshimanga 1 Jarre, Florian 1 Kim, Sunyoung 1 Kojima, Masakazu 1 Lescrenier, Marc J. A. 1 Lotan, Tsippy 1 Luo, ZiYan 1 Macieowski, J. M. 1 Murigande, Charles 1 Nash, Peter 1 Price, Christopher John 1 Pulleyblank, William R. 1 Qi, Liqun 1 Rincon-Camacho, Monserrat 1 Robinson, Daniel P. 1 Schnabel, Robert B. 1 Strodiot, Jean-Jacques 1 Tröltzsch, Anke 1 Tulkens, Henry 1 Wächter, Andreas 1 Walsham, G. 1 White, G. W. T. 1 Zarrop, Martin B. all top 5 Serials 27 Mathematical Programming. Series A. Series B 20 SIAM Journal on Optimization 17 Optimization Methods & Software 8 Mathematics of Computation 8 Computational Optimization and Applications 7 ACM Transactions on Mathematical Software 7 SIAM Journal on Numerical Analysis 5 IMA Journal of Numerical Analysis 4 Mathematical Programming 4 Numerische Mathematik 3 Journal of Optimization Theory and Applications 3 Journal of Complexity 3 SIAM Journal on Matrix Analysis and Applications 2 SIAM Journal on Scientific and Statistical Computing 2 Optimization 2 Annales de la Société Scientifique de Bruxelles. Série I 2 Numerical Linear Algebra with Applications 1 Inverse Problems 1 BIT 1 Systems & Control Letters 1 Journal of Computational Mathematics 1 Applied Numerical Mathematics 1 Transportation Science 1 Journal of Economic Dynamics & Control 1 Applied Mathematics Letters 1 Linear Algebra and its Applications 1 SIAM Journal on Scientific Computing 1 Optimization and Engineering 1 Foundations of Computational Mathematics 1 4OR 1 Acta Numerica 1 Computational Management Science 1 Networks and Spatial Economics 1 IEE Control Engineering Series 1 Springer Series in Computational Mathematics 1 Frontiers of Mathematics in China 1 MPS/SIAM Series on Optimization 1 Matapli 1 MOS/SIAM Series on Optimization 1 EURO Journal on Computational Optimization all top 5 Fields 148 Operations research, mathematical programming (90-XX) 114 Numerical analysis (65-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 17 Computer science (68-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Partial differential equations (35-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Statistics (62-XX) 3 Systems theory; control (93-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 156 Publications have been cited 4,619 times in 2,428 Documents Cited by ▼ Year ▼ Trust-region methods. Zbl 0958.65071Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 571 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 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. 166 1991 On the global convergence of a filter-SQP algorithm. Zbl 1029.65063Fletcher, Roger; Leyffer, Sven; Toint, Philippe L. 140 2002 CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Zbl 1325.90004Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L. 131 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 119 2002 LANCELOT. A Fortran package for large-scale nonlinear optimization (Release A). Zbl 0761.90087Conn, Andrew R.; Gould, Nick I. M.; Toint, Philippe L. 116 1992 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 an instance of the inverse shortest paths problem. Zbl 0756.90089Burton, D.; Toint, Ph. L. 103 1992 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 An assessment of nonmonotone linesearch techniques for unconstrained optimization. Zbl 0849.90113Toint, Philippe L. 99 1996 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. 80 2010 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. 67 2003 Recursive trust-region methods for multiscale nonlinear optimization. Zbl 1163.90024Gratton, Serge; Sartenaer, Annick; Toint, Philippe L. 63 2008 Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints. Zbl 0891.90153Toint, Philippe L. 63 1997 Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Zbl 1365.90236Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.; Toint, Ph. L. 60 2017 Global convergence of a class of trust-region methods for nonconvex minimization in Hilbert space. Zbl 0698.65043Toint, Ph. L. 57 1988 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 Local convergence analysis for partitioned quasi-Newton updates. Zbl 0505.65018Griewank, A.; Toint, Ph. L. 55 1982 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. 52 1988 Recent progress in unconstrained nonlinear optimization without derivatives. Zbl 0887.90154Conn, A. R.; Scheinberg, K.; Toint, Ph. L. 51 1997 On the convergence of derivative-free methods for unconstrained optimization. Zbl 1042.90617Conn, Andrew; Scheinberg, Katya; Toint, Philippe 50 1997 A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. Zbl 1075.65075Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L. 47 2004 A filter-trust-region method for unconstrained optimization. Zbl 1122.90074Gould, Nick I. M.; Sainvitu, Caroline; Toint, Philippe L. 47 2005 On sparse and symmetric matrix updating subject to a linear equation. Zbl 0379.65034Toint, Ph. L. 43 1977 Towards an efficient sparsity exploiting Newton method for minimization. Zbl 0463.65045Toint, Ph. L. 43 1981 Nonlinear programming without a penalty function or a filter. Zbl 1216.90069Gould, N. I. M.; Toint, Ph. L. 42 2010 Partitioned variable metric updates for large structured optimization problems. Zbl 0482.65035Griewank, A.; Toint, Ph. L. 40 1982 On the use of an inverse shortest paths algorithm for recovering linearly correlated costs. Zbl 0795.90080Burton, D.; Toint, Ph. L. 38 1994 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 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 Numerical methods for large-scale nonlinear optimization. Zbl 1119.65337Gould, Nick; Orban, Dominique; Toint, Philippe 35 2005 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 the estimation of sparse Hessian matrices. Zbl 0426.65025Powell, M. J. D.; Toint, Ph. L. 31 1979 Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. Zbl 1209.65017Scheinberg, K.; Toint, Ph. L. 29 2010 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 An algorithm using quadratic interpolation for unconstrained derivative free optimization. Zbl 0976.90102Conn, Andrew R.; Toint, Philippe L. 27 1996 Some numerical results using a sparse matrix updating formula in unconstrained optimization. Zbl 0381.65036Toint, Ph. L. 26 1978 Transfers to sustain dynamic core-theoretic cooperation in international stock pollutant control. Zbl 1179.91203Germain, Marc; Toint, Philippe; Tulkens, Henry; De Zeeuw, Aart 26 2003 On the unconstrained optimization of partially separable functions. Zbl 0563.90085Griewank, A.; Toint, Ph. L. 24 1982 An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Zbl 1229.90138Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke 22 2011 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 An adaptive Monte Carlo algorithm for computing mixed logit estimators. Zbl 1136.62086Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L. 22 2006 Global convergence of the partitioned BFGS algorithm for convex partially separable optimization. Zbl 0626.90076Toint, Ph. L. 21 1986 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 globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. Zbl 0854.90125Conn, A. R.; Gould, Nick; Toint, Ph. L. 21 1997 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 Convergence theory for nonconvex stochastic programming with an application to mixed logit. Zbl 1130.90371Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L. 21 2006 Numerical solution of large sets of algebraic nonlinear equations. Zbl 0614.65058Toint, Ph. L. 21 1986 The inverse shortest paths problem with upper bounds on shortest paths costs. Zbl 0878.90098Burton, D.; Pulleyblank, W. R.; Toint, Ph. L. 20 1997 Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Phillipe L. 20 2005 Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization. Zbl 1270.90078Toint, Philippe L. 20 2013 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 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 Universal regularization methods: varying the power, the smoothness and the accuracy. Zbl 1436.90136Cartis, Coralia; Gould, Nick I.; Toint, Philippe L. 18 2019 Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models. Zbl 1335.90094Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.; Toint, Ph. L. 17 2016 Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Zbl 1190.90209Gratton, Serge; Mouffe, Mélodie; Sartenaer, Annick; Toint, Philippe L.; Tomanos, Dimitri 15 2010 BFO, a trainable derivative-free brute force optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables. Zbl 1484.65136Porcelli, Margherita; Toint, Philippe L. 15 2017 Second-order optimality and beyond: characterization and evaluation complexity in convexly constrained nonlinear optimization. Zbl 1405.90125Cartis, Coralia; Gould, Nick I. M.; Toint, Philippe L. 15 2018 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 Preprocessing for quadratic programming. Zbl 1146.90491Gould, Nick; Toint, Philippe L. 14 2004 On large scale nonlinear network optimization. Zbl 0693.90092Toint, Ph. L.; Tuyttens, D. 14 1990 Adaptive regularization algorithms with inexact evaluations for nonconvex optimization. Zbl 1427.90228Bellavia, Stefania; Gurioli, Gianmarco; Morini, Benedetta; Toint, Philippe L. 13 2019 Numerical experiments with the Lancelot package (Release \(A\)) for large-scale nonlinear optimization. Zbl 0848.90109Conn, A. R.; Gould, Nick; Toint, Ph. L. 13 1996 A recursive \(\ell_{\infty}\)-trust-region method for bound-constrained nonlinear optimization. Zbl 1156.65060Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.; Weber-Mendonça, Melissa 12 2008 On the superlinear convergence of an algorithm for solving a sparse minimization problem. Zbl 0426.65024Toint, Ph. 12 1979 Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Zbl 1252.90061Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. 12 2012 Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints. Zbl 0806.90111Conn, A. R.; Gould, Nick; Sartenaer, A.; Toint, Ph. L. 11 1993 Approximate norm descent methods for constrained nonlinear systems. Zbl 1383.65051Morini, Benedetta; Porcelli, Margherita; Toint, Philippe L. 11 2018 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 On iterative algorithms for linear least squares problems with bound constraints. Zbl 0722.65019Bierlaire, M.; Toint, Ph. L.; Tuyttens, D. 11 1991 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 On large scale nonlinear least squares calculations. Zbl 0616.65014Toint, Ph. L. 11 1987 Convergence properties of minimization algorithms for convex constraints using a structured trust region. Zbl 0868.90106Conn, A. R.; Gould, Nick; Sartenaer, A.; Toint, Ph. L. 10 1996 Numerical experiments with partially separable optimization problems. Zbl 0531.65033Griewank, A.; Toint, Ph. L. 10 1984 A note about sparsity exploiting quasi-Newton updates. Zbl 0463.90081Toint, Ph. 10 1981 On the existence of convex decompositions of partially separable functions. Zbl 0561.65045Griewank, A.; Toint, Ph. L. 10 1984 Worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization. Zbl 1342.90180Cartis, C.; Sampaio, Ph. R.; Toint, Ph. L. 10 2015 An iterative working-set method for large-scale nonconvex quadratic programming. Zbl 1012.65054Gould, Nicholas I. M.; Toint, Philippe L. 9 2002 Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019Cartis, C.; Gould, N. I. M.; Toint, P. L. 9 2009 A note on the convergence of barrier algorithms to second-order necessary points. Zbl 0954.90052Gould, Nicholas I. M.; Toint, Philippe L. 8 1999 Performance of a multifrontal scheme for partially separable optimization. Zbl 0809.90117Conn, A. R.; Gould, Nick; Lescrenier, M.; Toint, Ph. L. 8 1994 Optimizing partially separable functions without derivatives. Zbl 1152.90659Colson, Benoît; Toint, Philippe L. 8 2005 A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Zbl 1311.90187Sampaio, Ph. R.; Toint, Ph. L. 8 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 Recognizing underlying sparsity in optimization. Zbl 1163.90026Kim, Sunyoung; Kojima, Masakazu; Toint, Philippe 7 2009 Complexity of partially separable convexly constrained optimization with non-Lipschitzian singularities. Zbl 1411.90318Chen, Xiaojun; Toint, Ph. L.; Wang, H. 7 2019 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 filter-trust-region method for simple-bound constrained optimization. Zbl 1169.90458Sainvitu, Caroline; Toint, Philippe L. 6 2007 A retrospective trust-region method for unconstrained optimization. Zbl 1196.65101Bastin, Fabian; Malmedy, Vincent; Mouffe, Mélodie; Toint, Philippe L.; Tomanos, Dimitri 6 2010 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 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 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 Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculations. Zbl 0554.65085Goldfarb, D.; Toint, Ph. L. 5 1984 An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity. Zbl 1465.90071Gratton, S.; Simon, E.; Toint, Ph. L. 5 2021 High-order evaluation complexity for convexly-constrained optimization with non-Lipschitzian group sparsity terms. Zbl 1465.90095Chen, X.; Toint, Ph. L. 3 2021 Minimizing convex quadratics with variable precision conjugate gradients. Zbl 07332751Gratton, Serge; Simon, Ehouarn; Titley-Peloquin, David; Toint, Philippe L. 2 2021 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 Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments. Zbl 1440.15036Luo, Ziyan; Qi, Liqun; Toint, Philippe L. 2 2020 A note on solving nonlinear optimization problems in variable precision. Zbl 1446.90149Gratton, S.; Toint, Ph. L. 2 2020 Universal regularization methods: varying the power, the smoothness and the accuracy. Zbl 1436.90136Cartis, Coralia; Gould, Nick I.; Toint, Philippe L. 18 2019 Adaptive regularization algorithms with inexact evaluations for nonconvex optimization. Zbl 1427.90228Bellavia, Stefania; Gurioli, Gianmarco; Morini, Benedetta; Toint, Philippe L. 13 2019 Complexity of partially separable convexly constrained optimization with non-Lipschitzian singularities. Zbl 1411.90318Chen, Xiaojun; Toint, Ph. L.; Wang, H. 7 2019 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 A note on using performance and data profiles for training algorithms. Zbl 1471.68328Porcelli, Margherita; Toint, Philippe L. 2 2019 Second-order optimality and beyond: characterization and evaluation complexity in convexly constrained nonlinear optimization. Zbl 1405.90125Cartis, Coralia; Gould, Nick I. M.; Toint, Philippe L. 15 2018 Approximate norm descent methods for constrained nonlinear systems. Zbl 1383.65051Morini, Benedetta; Porcelli, Margherita; Toint, Philippe L. 11 2018 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 Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Zbl 1365.90236Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.; Toint, Ph. L. 60 2017 BFO, a trainable derivative-free brute force optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables. Zbl 1484.65136Porcelli, Margherita; Toint, Philippe L. 15 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 Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models. Zbl 1335.90094Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.; Toint, Ph. L. 17 2016 Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints. Zbl 1369.90138Sampaio, Ph. R.; Toint, Ph. L. 5 2016 Simple examples for the failure of Newton’s method with line search for strictly convex minimization. Zbl 1346.90665Jarre, Florian; Toint, Philippe L. 2 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. 131 2015 Worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization. Zbl 1342.90180Cartis, C.; Sampaio, Ph. R.; Toint, Ph. L. 10 2015 A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Zbl 1311.90187Sampaio, Ph. R.; Toint, Ph. L. 8 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 Quasi-Newton updates with weighted secant equations. Zbl 1356.90162Gratton, S.; Malmedy, V.; Toint, Ph. L. 4 2015 An interior-point \(\ell_1\)-penalty method for nonlinear optimization. Zbl 1330.65085Gould, Nick I. M.; Orban, Dominique; Toint, Philippe L. 4 2015 Observation thinning in data assimilation computations. Zbl 1307.90104Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Philippe L. 1 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 Differentiating the method of conjugate gradients. Zbl 1306.65180Gratton, Serge; Titley-Peloquin, David; Toint, Philippe; Ilunga, Jean Tshimanga 2 2014 Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization. Zbl 1270.90078Toint, Philippe L. 20 2013 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 Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. Zbl 1267.90093Gratton, Serge; Gürol, Selime; Toint, Philippe L. 2 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 Erratum to: “Nonlinear programming without a penalty function or a filter”. Zbl 1235.90118Gould, N. I. M.; Toint, Ph. L. 3 2012 A model of weekly labor participation for a Belgian synthetic population. Zbl 1332.91094Cirillo, Cinzia; Cornelis, Eric; Toint, Philippe L. 2 2012 Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Zbl 1245.90122Gratton, Serge; Malmedy, Vincent; Toint, Philippe L. 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 An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Zbl 1229.90138Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke 22 2011 Stopping rules and backward error analysis for bound-constrained optimization. Zbl 1228.65088Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L. 3 2011 Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. Zbl 1237.65033Gratton, S.; Toint, Ph. L.; Ilunga, J. Tshimanga 2 2011 Approximating Hessians in unconstrained optimization arising from discretized problems. Zbl 1228.90117Malmedy, Vincent; Toint, Philippe L. 1 2011 Fast regularized linear sampling for inverse scattering problems. Zbl 1245.65121Fares, M’Barek; Gratton, Serge; Toint, Philippe L. 1 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. 80 2010 Nonlinear programming without a penalty function or a filter. Zbl 1216.90069Gould, N. I. M.; Toint, Ph. L. 42 2010 Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. Zbl 1209.65017Scheinberg, K.; Toint, Ph. L. 29 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 Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Zbl 1190.90209Gratton, Serge; Mouffe, Mélodie; Sartenaer, Annick; Toint, Philippe L.; Tomanos, Dimitri 15 2010 A retrospective trust-region method for unconstrained optimization. Zbl 1196.65101Bastin, Fabian; Malmedy, Vincent; Mouffe, Mélodie; Toint, Philippe L.; Tomanos, Dimitri 6 2010 Approximate invariant subspaces and quasi-Newton optimization methods. Zbl 1202.90272Gratton, Serge; Toint, Philippe L. 2 2010 Formulation and solution strategies for nonparametric nonlinear stochastic programmes with an application in finance. Zbl 1202.90202Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L. 1 2010 Trust-region and other regularisations of linear least-squares problems. Zbl 1165.65019Cartis, C.; Gould, N. I. M.; Toint, P. L. 9 2009 Recognizing underlying sparsity in optimization. Zbl 1163.90026Kim, Sunyoung; Kojima, Masakazu; Toint, Philippe 7 2009 SVD-tail: A new linear-sampling reconstruction method for inverse scattering problems. Zbl 1175.65129Fares, M’Barek; Gratton, Serge; Toint, Philippe L. 3 2009 A multilevel algorithm for solving the trust-region subproblem. Zbl 1179.90315Toint, Philippe L.; Tomanos, D.; Weber-Mendonça, M. 1 2009 Recursive trust-region methods for multiscale nonlinear optimization. Zbl 1163.90024Gratton, Serge; Sartenaer, Annick; Toint, Philippe L. 63 2008 A recursive \(\ell_{\infty}\)-trust-region method for bound-constrained nonlinear optimization. Zbl 1156.65060Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.; Weber-Mendonça, Melissa 12 2008 A filter-trust-region method for simple-bound constrained optimization. Zbl 1169.90458Sainvitu, Caroline; Toint, Philippe L. 6 2007 An adaptive Monte Carlo algorithm for computing mixed logit estimators. Zbl 1136.62086Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L. 22 2006 Convergence theory for nonconvex stochastic programming with an application to mixed logit. Zbl 1130.90371Bastin, Fabian; Cirillo, Cinzia; Toint, Philippe L. 21 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 Exploiting problem structure in pattern search methods for unconstrained optimization. Zbl 1136.90516Price, C. J.; Toint, Ph. L. 4 2006 Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Zbl 1132.65054Gratton, Serge; Sartenaer, Annick; Toint, Philippe L. 1 2006 A filter-trust-region method for unconstrained optimization. Zbl 1122.90074Gould, Nick I. M.; Sainvitu, Caroline; Toint, Philippe L. 47 2005 Numerical methods for large-scale nonlinear optimization. Zbl 1119.65337Gould, Nick; Orban, Dominique; Toint, Philippe 35 2005 Sensitivity of trust-region algorithms to their parameters. Zbl 1086.65060Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Phillipe L. 20 2005 Optimizing partially separable functions without derivatives. Zbl 1152.90659Colson, Benoît; Toint, Philippe L. 8 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 Preprocessing for quadratic programming. Zbl 1146.90491Gould, Nick; Toint, Philippe L. 14 2004 How mature is nonlinear optimization? Zbl 1146.90515Gould, Nick; Toint, Philippe L. 1 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. 67 2003 Transfers to sustain dynamic core-theoretic cooperation in international stock pollutant control. Zbl 1179.91203Germain, Marc; Toint, Philippe; Tulkens, Henry; De Zeeuw, Aart 26 2003 Global convergence of a hybrid trust-region SQP-filter algorithm for general nonlinear programming. Zbl 1063.90052Gould, Nick; Toint, Philippe L. 3 2003 On the global convergence of a filter-SQP algorithm. Zbl 1029.65063Fletcher, Roger; Leyffer, Sven; Toint, Philippe L. 140 2002 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 119 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 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 Exploiting band structure in unconstrained optimization without derivatives. Zbl 1035.90083Colson, Benoît; Toint, Philippe L. 4 2001 Error analysis of signal zeros from a related companion matrix eigenvalue problem. Zbl 1037.65038Bazán, F. S. V.; Toint, Ph. L. 1 2001 Trust-region methods. Zbl 0958.65071Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 571 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 Conditioning of infinite Hankel matrices of finite rank. Zbl 0980.93028Bazán, F. S. V.; Toint, P. L. 3 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 A linesearch algorithm with memory for unconstrained optimization. Zbl 0942.65067Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L. 1 1998 Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints. Zbl 0891.90153Toint, Philippe L. 63 1997 ...and 56 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,853 Authors 69 Martínez, José Mario 69 Toint, Philippe L. 45 Zhu, Detong 40 Babaie-Kafaki, Saman 34 Birgin, Ernesto G. 33 Zhang, Jianzhong 31 Jian, Jinbao 28 Yuan, Gonglin 26 Andrei, Neculai 24 Amini, Keyvan 23 Gould, Nicholas Ian Mark 23 Santos, Sandra Augusta 23 Vicente, Luis Nunes 23 Wei, Zengxin 22 Dai, Yu-Hong 22 Gratton, Serge 22 Robinson, Daniel P. 22 Sun, Wenyu 21 Yuan, Ya-xiang 20 Cartis, Coralia 20 Kimiaei, Morteza 20 Orban, Dominique 20 Pu, Dingguo 18 Curtis, Frank E. 18 Lukšan, Ladislav 18 Morini, Benedetta 18 Nesterov, Yurii 17 Ni, Qin 17 Shen, Chungen 17 Zhang, Liwei 16 Audet, Charles 16 Bellavia, Stefania 16 Chen, Zhongwen 16 Grapiglia, Geovani Nunes 16 Nocedal, Jorge 16 Xiao, Yunhai 15 Dostál, Zdeněk 14 Ahookhosh, Masoud 14 Fasano, Giovanni 14 Ghanbari, Reza 14 Gu, Chao 14 Kanzow, Christian 14 Karas, Elizabeth W. 14 Leong, Wah June 13 Andreani, Roberto 13 Conn, Andrew Roger 13 Li, Donghui 13 Lucidi, Stefano 13 Salahi, Maziar 12 Aminifard, Zohre 12 Le Digabel, Sébastien 12 Leyffer, Sven 12 Liu, Zexian 12 Peyghami, Mohammad Reza 12 Shi, Zhenjun 12 Vlček, Jan 12 Zaccour, Georges 11 Marcia, Roummel F. 11 Porcelli, Margherita 11 Qi, Liqun 11 Roma, Massimo 11 Yu, Zhensheng 11 Zhang, Lei-Hong 10 Al-Baali, Mehiddin 10 Armand, Paul 10 Cheng, Wanyou 10 Fernandes, Edite M. G. P. 10 Griewank, Andreas 10 Krejić, Nataša 10 Ou, Yigui 10 Steihaug, Trond 10 Viloche Bazán, Fermín S. 10 Zhang, Hongchao 10 Zhang, Li 9 Byrd, Richard H. 9 Esmaeili, Hamid 9 Jiang, Xianzhen 9 Li, Min 9 Su, Ke 9 Wang, Fusheng 9 Wang, Zhujun 9 Xia, Yong 9 Xu, Chengxian 9 Yao, Shengwei 8 di Serafino, Daniela 8 Diehl, Moritz Mathias 8 Erway, Jennifer B. 8 Hare, Warren L. 8 Huang, Yakui 8 Liu, Hongwei 8 Luo, Xinlong 8 Mahdavi-Amiri, Nezam 8 Qiu, Songqiang 8 Riccietti, Elisa 8 Royer, Clément W. 8 Sahinidis, Nikolaos V. 8 Schuverdt, María Laura 8 Shanno, David F. 8 Tang, Chunming 8 Wächter, Andreas ...and 2,753 more Authors all top 5 Cited in 265 Serials 186 Computational Optimization and Applications 170 Optimization Methods & Software 156 Mathematical Programming. Series A. Series B 146 Journal of Optimization Theory and Applications 113 Journal of Computational and Applied Mathematics 99 Applied Mathematics and Computation 92 SIAM Journal on Optimization 79 Numerical Algorithms 76 Journal of Global Optimization 62 Optimization 60 Optimization Letters 45 European Journal of Operational Research 36 Computational and Applied Mathematics 35 International Journal of Computer Mathematics 33 Optimization and Engineering 31 Computers & Mathematics with Applications 31 Journal of Applied Mathematics and Computing 28 Numerical Functional Analysis and Optimization 27 Applied Numerical Mathematics 24 Computer Methods in Applied Mechanics and Engineering 23 Mathematical Programming Computation 22 Mathematics of Computation 22 SIAM Journal on Scientific Computing 22 Journal of Industrial and Management Optimization 21 Annals of Operations Research 21 Mathematical Problems in Engineering 19 Applied Mathematical Modelling 16 Mathematical Programming 15 Linear Algebra and its Applications 14 Numerische Mathematik 14 Asia-Pacific Journal of Operational Research 14 Journal of Systems Science and Complexity 13 Journal of Scientific Computing 13 Abstract and Applied Analysis 13 Mathematical Methods of Operations Research 13 Journal of Inequalities and Applications 12 Calcolo 11 Discrete Applied Mathematics 11 Automatica 11 SIAM Journal on Matrix Analysis and Applications 11 Journal of Applied Mathematics 10 Operations Research Letters 10 Computers & Operations Research 10 Applied Mathematics Letters 10 Computational Geosciences 10 Science China. Mathematics 9 Journal of Computational Physics 9 BIT 9 Acta Mathematicae Applicatae Sinica. English Series 9 Applied Mathematics. Series B (English Edition) 8 Applied Mathematics and Optimization 8 Computing 8 International Journal for Numerical Methods in Engineering 8 Mathematics of Operations Research 8 Journal of Economic Dynamics & Control 8 Top 8 Acta Mathematica Sinica. English Series 8 RAIRO. Operations Research 8 4OR 8 Numerical Algebra, Control and Optimization 8 Journal of the Operations Research Society of China 7 EURO Journal on Computational Optimization 6 Theoretical Computer Science 6 Structural and Multidisciplinary Optimization 5 Kybernetika 5 Operations Research 5 SIAM Review 5 Numerical Linear Algebra with Applications 5 Journal of Combinatorial Optimization 5 SIAM Journal on Imaging Sciences 4 Inverse Problems 4 Journal of Mathematical Analysis and Applications 4 SIAM Journal on Control and Optimization 4 Science in China. Series A 4 INFORMS Journal on Computing 4 Soft Computing 4 Discrete Dynamics in Nature and Society 4 International Journal of Applied Mathematics and Computer Science 4 Computational Management Science 4 Journal of Mathematical Modeling 3 Networks 3 SIAM Journal on Numerical Analysis 3 Bulletin of the Iranian Mathematical Society 3 Journal of Complexity 3 Computational Mechanics 3 Neural Computation 3 Applications of Mathematics 3 Automation and Remote Control 3 International Journal of Robust and Nonlinear Control 3 Journal of Mathematical Imaging and Vision 3 Advances in Computational Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Foundations of Computational Mathematics 3 Discrete Optimization 3 Engineering Optimization 3 Frontiers of Mathematics in China 3 Set-Valued and Variational Analysis 3 Asian Journal of Control 3 Statistics and Computing 2 International Journal of Control ...and 165 more Serials all top 5 Cited in 43 Fields 2,023 Operations research, mathematical programming (90-XX) 1,219 Numerical analysis (65-XX) 397 Calculus of variations and optimal control; optimization (49-XX) 132 Computer science (68-XX) 74 Systems theory; control (93-XX) 64 Mechanics of deformable solids (74-XX) 54 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 41 Statistics (62-XX) 37 Information and communication theory, circuits (94-XX) 35 Fluid mechanics (76-XX) 34 Partial differential equations (35-XX) 32 Biology and other natural sciences (92-XX) 28 Combinatorics (05-XX) 20 Operator theory (47-XX) 14 Ordinary differential equations (34-XX) 14 Probability theory and stochastic processes (60-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Geophysics (86-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Real functions (26-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Approximations and expansions (41-XX) 7 Quantum theory (81-XX) 6 Functional analysis (46-XX) 6 Mechanics of particles and systems (70-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 Convex and discrete geometry (52-XX) 4 Optics, electromagnetic theory (78-XX) 3 Number theory (11-XX) 3 Integral equations (45-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Difference and functional equations (39-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Mathematics education (97-XX) Citations by Year