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:
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)
Second-Order Optimality and Beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization
Foundations of Computational Mathematics
page 1-35
(7 September 2017)
Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
Mathematical Programming
page 1-39
(1 April 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.