Research Interests
 algorithm design, analysis and implementation for linear and nonlinear nonconvex smooth optimization, suitable for largescale problems
 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
 C. Cartis and Y. Yan
Active set prediction for interior point methods using controlled perturbations
Technical Report NA14/07, Mathematical Institute, University of Oxford, 2014.
Associated software : PIPM (author: Yiming Yan)  C. Cartis and A. Thompson
A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing
Technical Report NA13/20, Mathematical Institute, University of Oxford, 2013.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the evaluation complexity of constrained nonlinear leastsquares and general constrained nonlinear optimization using secondorder methods
ERGO Technical Report 13005, School of Mathematics, Edinburgh University, 2013.  C. Cartis, N. I. M. Gould and Ph. L. Toint
Optimal Newtontype methods for nonconvex smooth optimization problems
ERGO Technical Report 11009, School of Mathematics, Edinburgh University, 2011.  C. Cartis, J. M. Fowkes and N. I. M. Gould
Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties
Journal of Global Optimization, vol. 61(3):429457, 2015. (DOI) 10.1007/s1089801401996.  C. Cartis, N. I. M. Gould and Ph. L. Toint.
On the complexity of finding firstorder critical points in constrained nonlinear programming.
Mathematical Programming Series A, vol. 144(12):93106, 2014. (DOI) 10.1007/s1010701206179  C. Cartis, Ph. R. Sampaio and Ph. L. Toint
Worstcase evaluation complexity of nonmonotone gradientrelated algorithms for unconstrained optimization
Optimization, (DOI) 10.1080/02331934.2013.869809, 2014 (online first).  C. Cartis and A. Thompson
An exact tree projection algorithm for wavelets
IEEE Signal Processing Letters, vol. 20(11):10261029, 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
Journal of Climate, vol. 26(23):93489366, 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
Journal of Climate, vol. 26(23):93679383, 2013.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the evaluation complexity of cubic regularization methods for potentially rankdeficient nonlinear
leastsquares problems and its relevance to constrained nonlinear optimization
SIAM Journal on Optimization, vol. 23(3):15531574, 2013. (doi: 10.1137/120869687)  C. Cartis, N. I. M. Gould and Ph. L. Toint
A note about the complexity of minimizing Nesterov's smooth ChebyshevRosenbrock function
Optimization Methods and Software, vol. 28(3):451457, 2013.  C. Cartis, N. I. M. Gould and Ph. L. Toint
How much patience do you have? A worstcase 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
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its functionevaluation complexity
IMA Journal on Numerical Analysis, vol. 32(4):16621695, 2012.  C. Cartis, N. I. M. Gould and Ph. L. Toint
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
Optimization Methods and Software, vol. 27(2), pp. 197219, 2012.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the oracle complexity of firstorder and derivativefree algorithms for smooth nonconvex minimization
SIAM Journal on Optimization, vol. 22(1), pp. 6686, 2012.  C. Cartis, N. I. M. Gould and Ph. L. Toint
Complexity bounds for secondorder optimality in unconstrained optimization
Journal of Complexity, vol. 28(1), pp. 93108, 2012.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
SIAM Journal on Optimization, vol. 21(4), pp. 17211739, 2011.  C. Cartis, N. I. M. Gould and Ph. L. Toint
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worstcase function and derivativeevaluation complexity
Mathematical Programming, vol. 130(2), pp. 295319, 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. 245295, 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. 188203, 2011.  J. D. Blanchard, C. Cartis and J. Tanner
Compressed sensing: how sharp is the restricted isometry property?
SIAM Review, vol. 53(1), pp. 105125, 2011.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization
SIAM Journal on Optimization, vol. 20(6), pp. 28332852, 2010.  S. Bellavia, C. Cartis, N. I. M. Gould, B. Morini and Ph. L. Toint
Convergence of a regularized Euclidean residual algorithm for nonlinear leastsquares
SIAM Journal on Numerical Analysis, vol. 48(1), pp. 129, 2010.  J. D. Blanchard, C. Cartis and J. Tanner
Decay properties for restricted isometry constants
IEEE Signal Processing Letters, vol. 16(7), pp. 572575, 2009.  C. Cartis, N. I. M. Gould and Ph. L. Toint
Trustregion and other regularisations of linear leastsquares problems
BIT, vol. 49(1), pp. 2153, 2009.  C. Cartis
Some disadvantages of a Mehrotratype primaldual corrector interior point algorithm for linear programming
Applied Numerical Mathematics, vol. 59, pp. 11101119, 2009.  C. Cartis, N. I. M. Gould and Ph. L. Toint
An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian
ERGO Technical Report 13008, School of Mathematics, Edinburgh University, 2013.  C. Cartis, N. I. M. Gould and Ph. L. Toint
On the complexity of steepest descent method with exact linesearches
ERGO Technical Report 12009, School of Mathematics, Edinburgh University, 2012.  C. Cartis and R. Hauser. A new perspective on the complexity of interior point methods for linear programming. Technical Report 07/05, Numerical Analysis Group, Computing Laboratory, Oxford University, 26 pages, 2007.
 C. Cartis and N. I. M. Gould. Finding a point in the relative interior of a polyhedron. Technical Report RAL 2006016, Rutherford Appleton Laboratory, 57 pages, 2006.
 C. Cartis. On the convergence of a primaldual secondorder corrector interior point algorithm for linear programming. Technical Report 05/04, Numerical Analysis Group, Computing Laboratory, 35 pages, 2005.
 C. Cartis and A. Thompson. A new recovery analysis for iterative hard thresholding for compressed sensing. Proceedings of SPARS'11 (Signal Processing with Adaptive Sparse Structured Representations), Edinburgh (UK), April 2011.
 C. Cartis and N. I. M. Gould. Finding a point in the relative interior of a polyhedron, with applications to compressed sensing. Proceedings of SPARS'09 (Signal Processing with Adaptive Sparse Structured Representations), SaintMalo (France), April 2009.
 J. D. Blanchard, C. Cartis and J. Tanner. Phase transitions for restricted isometry properties. Proceedings of SPARS'09 (Signal Processing with Adaptive Sparse Structured Representations), SaintMalo (France), April 2009.
 C. Cartis. On Interior Point Methods for Linear Programming, DAMTP, University of Cambridge, 2005.
(available upon request)
Software

Some of my algorithms have been implemented into GALAHAD  a principal optimization software library.
Software outcome of EPSRC project EP/I028854/1: Global optimization software package oBB
oBB now part of COINOR: oBB on COINOR