Status:
Associate Professor in Numerical Optimization, Mathematical Institute
Tutorial Fellow in Mathematics, Balliol College
Personal website:
+44 1865 273526
ORCID iD:
https://orcid.org/0000-0002-0963-5550
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Recent Publications:
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
Approximation and Optimization - Algorithms, Complexity and Applications
(1 January 2019)
UNIVERSAL REGULARIZATION METHODS: VARYING THE POWER, THE SMOOTHNESS AND THE ACCURACY
SIAM JOURNAL ON OPTIMIZATION
issue 1
volume 29
page 595-615
(2019)
Full text available
Global rates of convergence for nonconvex optimization on manifolds
IMA Journal of Numerical Analysis
issue 1
volume 39
page 1-33
(1 January 2019)
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization.
Journal of Complexity
volume abs/1705.07285
(November 2018)
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)
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.