Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results C Cartis, NIM Gould, PL Toint Mathematical Programming 127 (2), 245-295, 2011 | 324 | 2011 |

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function-and derivative-evaluation complexity C Cartis, NIM Gould, PL Toint Mathematical programming 130 (2), 295-319, 2011 | 241 | 2011 |

On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization problems C Cartis, NIM Gould, PL Toint Siam journal on optimization 20 (6), 2833-2852, 2010 | 213 | 2010 |

Global rates of convergence for nonconvex optimization on manifolds N Boumal, PA Absil, C Cartis IMA Journal of Numerical Analysis 39 (1), 1-33, 2019 | 185 | 2019 |

Compressed sensing: How sharp is the restricted isometry property JD Blanchard, C Cartis, J Tanner Arxiv preprint arXiv:1004.5026, 2010 | 180 | 2010 |

Global convergence rate analysis of unconstrained optimization methods based on probabilistic models C Cartis, K Scheinberg Mathematical Programming 169 (2), 337-375, 2018 | 91 | 2018 |

Complexity bounds for second-order optimality in unconstrained optimization C Cartis, NIM Gould, PL Toint Journal of Complexity 28 (1), 93-108, 2012 | 90 | 2012 |

On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming C Cartis, NIM Gould, PL Toint SIAM Journal on Optimization 21 (4), 1721-1739, 2011 | 89 | 2011 |

Convergence rate analysis of a stochastic trust-region method via supermartingales J Blanchet, C Cartis, M Menickelly, K Scheinberg INFORMS journal on optimization 1 (2), 92-119, 2019 | 72* | 2019 |

An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity C Cartis, NIM Gould, PL Toint IMA Journal of Numerical Analysis 32 (4), 1662-1695, 2012 | 72 | 2012 |

Phase transitions for greedy sparse approximation algorithms JD Blanchard, C Cartis, J Tanner, A Thompson Applied and Computational Harmonic Analysis 30 (2), 188-203, 2011 | 69 | 2011 |

Improving the flexibility and robustness of model-based derivative-free optimization solvers C Cartis, J Fiala, B Marteau, L Roberts ACM Transactions on Mathematical Software (TOMS) 45 (3), 1-41, 2019 | 61 | 2019 |

On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization C Cartis, NIM Gould, PL Toint SIAM Journal on Optimization 22 (1), 66-86, 2012 | 55 | 2012 |

On the complexity of finding first-order critical points in constrained nonlinear optimization C Cartis, NIM Gould, PL Toint Mathematical Programming 144 (1), 93-106, 2014 | 54 | 2014 |

On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization C Cartis, NIM Gould, PL Toint SIAM Journal on Optimization 23 (3), 1553-1574, 2013 | 51 | 2013 |

Toint. Adaptive cubic regularisation methods for unconstrained optimization. part ii: worst-case function-and derivative-evaluation complexity C Cartis, NIM Gould, L Philippe Mathematical programming 130 (2), 295-319, 2011 | 49 | 2011 |

Trust-region and other regularisations of linear least-squares problems C Cartis, NIM Gould, PL Toint BIT Numerical Mathematics 49 (1), 21-53, 2009 | 48 | 2009 |

Can top-of-atmosphere radiation measurements constrain climate predictions? Part I: Tuning SFB Tett, MJ Mineter, C Cartis, DJ Rowlands, P Liu Journal of Climate 26 (23), 9348-9366, 2013 | 41* | 2013 |

Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares S Bellavia, C Cartis, NIM Gould, B Morini, PL Toint SIAM Journal on Numerical Analysis 48 (1), 1-29, 2010 | 41 | 2010 |

Universal regularization methods: varying the power, the smoothness and the accuracy C Cartis, NI Gould, PL Toint SIAM Journal on Optimization 29 (1), 595-615, 2019 | 39 | 2019 |