Associate Professor in Numerical Optimization, Mathematical Institute
Tutorial Fellow in Mathematics, Balliol College
Personal Website:
+44 1865 273526
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Recent Publications:
Second-Order Optimality and Beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization
Foundations of Computational Mathematics
issue 5
volume 18
page 1073-1107
(1 October 2018)
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
Proceedings of the ICM
(3 May 2018)
Global rates of convergence for nonconvex optimization on manifolds
IMA Journal of Numerical Analysis
(7 February 2018)
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
Optimization Methods and Software
issue 6
volume 32
page 1273-1298
(2 November 2017)
Calibrating Climate Models Using Inverse Methods: Case studies with HadAM3, HadAM3P and HadCM3
Geoscientific Model Development
page 1-36
(28 September 2017)
Research Interests:
Algorithm design, analysis and implementation for linear and nonlinear optimization, convex and nonconvex problems, large-scale
- Complexity of optimization problems and algorithms
- Interconnections between dynamical systems and continuous optimization
- Applications: compressed sensing and sparse approximation
- Applications: inverse problems in climate modelling
Prizes, Awards, and Scholarships:
Leslie Fox Prize in Numerical Analysis 2005 (second place)
Major / Recent Publications:
- C. Cartis and A. Thompson
An exact tree projection algorithm for wavelets
ERGO Technical Report 13-006, School of Mathematics, Edinburgh University, 2013.
To appear in IEEE Signal Processing Letters (2013) - S. F. B. Tett, M. J. Mineter, C. Cartis, D. J. Rowlands and P. Liu
Can top of atmosphere radiation measurements constrain climate predictions? Part 1: Tuning
To appear in Journal of Climate (2013) - S. F. B. Tett, D. J. Rowlands, M. J. Mineter and C. Cartis
Can top of atmosphere radiation measurements constrain climate predictions? Part 2: Climate Sensitivity
To appear in Journal of Climate (2013) - C. Cartis, N. I. M. Gould and Ph. L. Toint
On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear
least-squares problems and its relevance to constrained nonlinear optimization
SIAM Journal on Optimization, vol. 23(3):1553--1574, 2013. (doi: 10.1137/120869687)
- C. Cartis, N. I. M. Gould and Ph. L. Toint
How much patience do you have? A worst-case perspective on smooth nonconvex optimization
OPTIMA 88, 2012. (feature article of the Mathematical Optimization Society Newsletter) - C. Cartis, N. I. M. Gould and Ph. L. Toint.
On the complexity of finding first-order critical points in constrained nonlinear programming.
Mathematical Programming Series A, (DOI) 10.1007/s10107-012-0617-9 (Online First, 2012)
- C. Cartis, N. I. M. Gould and Ph. L. Toint
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity
Mathematical Programming, vol. 130(2), pp. 295--319, 2011. - C. Cartis, N. I. M. Gould and Ph. L. Toint
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
Mathematical Programming, vol. 127(2), pp. 245--295, 2011.
- J. D. Blanchard, C. Cartis, J. Tanner and A. Thompson
Phase transitions for greedy sparse approximation algorithms
Applied and Computational Harmonic Analysis, vol. 30(2), pp. 188--203, 2011. - J. D. Blanchard, C. Cartis and J. Tanner
Compressed sensing: how sharp is the restricted isometry property?
SIAM Review, vol. 53(1), pp. 105--125, 2011.