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 | 474 | 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 | 369 | 2011 |

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 | 320 | 2019 |

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 | 285 | 2010 |

Compressed sensing: How sharp is the restricted isometry property JD Blanchard, C Cartis, J Tanner Arxiv preprint arXiv:1004.5026, 2010 | 215* | 2010 |

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 | 182 | 2019 |

Global convergence rate analysis of unconstrained optimization methods based on probabilistic models C Cartis, K Scheinberg Mathematical Programming 169, 337-375, 2018 | 162 | 2018 |

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 | 149* | 2019 |

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 | 133 | 2011 |

Complexity bounds for second-order optimality in unconstrained optimization C Cartis, NIM Gould, PL Toint Journal of Complexity 28 (1), 93-108, 2012 | 115 | 2012 |

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 | 94 | 2012 |

Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints C Cartis, NIM Gould, PL Toint SIAM Journal on Optimization 30 (1), 513-541, 2020 | 89* | 2020 |

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 | 76 | 2012 |

Escaping local minima with local derivative-free methods: a numerical investigation C Cartis, L Roberts, O Sheridan-Methven Optimization 71 (8), 2343-2373, 2022 | 71 | 2022 |

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 | 71 | 2011 |

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 | 68 | 2014 |

Adaptive regularization with cubics on manifolds N Agarwal, N Boumal, B Bullins, C Cartis Mathematical Programming 188, 85-134, 2021 | 66* | 2021 |

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 | 64 | 2019 |

A derivative-free Gauss–Newton method C Cartis, L Roberts Mathematical Programming Computation 11, 631-674, 2019 | 62 | 2019 |

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 | 62 | 2013 |