Research Interests
- algorithm design, analysis and implementation for linear and nonlinear nonconvex smooth optimization, suitable for large-scale 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
Some of my algorithms have been implemented into GALAHAD --- a principal optimization software library.
New!
- 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 steepest descent method with exact linesearches
ERGO Technical Report 12-009, School of Mathematics, Edinburgh University, 2012.
Under Review
- 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, 2012
Collaboration with School of GeoSciences, University of Edinburgh (Ping Liu - OR MSc student 09/10, School of Mathematics).
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, 2012. - 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
ERGO Technical Report 12-001, School of Mathematics, Edinburgh University, 2012. - C. Cartis, N. I. M. Gould and Ph. L. Toint
Optimal Newton-type methods for nonconvex smooth optimization problems
ERGO Technical Report 11-009, School of Mathematics, Edinburgh University, 2011.
Journal Articles
- 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
A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
Optimization Methods and Software, doi: 10.1080/10556788.2012.722632 (to appear in print, 2013). - C. Cartis, N. I. M. Gould and Ph. L. Toint
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
IMA Journal on Numerical Analysis, vol. 32(4):1662--1695, 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. 197--219, 2012. - C. Cartis, N. I. M. Gould and Ph. L. Toint
On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
SIAM Journal on Optimization, vol. 22(1), pp. 66--86, 2012. - C. Cartis, N. I. M. Gould and Ph. L. Toint
Complexity bounds for second-order optimality in unconstrained optimization
Journal of Complexity, vol. 28(1), pp. 93--108, 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. 1721--1739, 2011. - 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. - 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. 2833--2852, 2010. - S. Bellavia, C. Cartis, N. I. M. Gould, B. Morini and Ph. L. Toint
Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares
SIAM Journal on Numerical Analysis, vol. 48(1), pp. 1--29, 2010. - J. D. Blanchard, C. Cartis and J. Tanner
Decay properties for restricted isometry constants
IEEE Signal Processing Letters, vol. 16(7), pp. 572--575, 2009. - C. Cartis, N. I. M. Gould and Ph. L. Toint
Trust-region and other regularisations of linear least-squares problems
BIT, vol. 49(1), pp. 21--53, 2009. - C. Cartis
Some disadvantages of a Mehrotra-type primal-dual corrector interior point algorithm for linear programming
Applied Numerical Mathematics, vol. 59, pp. 1110--1119, 2009.
Technical Reports
- 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 2006-016, Rutherford Appleton Laboratory, 57 pages, 2006.
- C. Cartis. On the convergence of a primal-dual second-order corrector interior point algorithm for linear programming. Technical Report 05/04, Numerical Analysis Group, Computing Laboratory, 35 pages, 2005.
Conference Proceedings (refereed)
- 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), Saint-Malo (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), Saint-Malo (France), April 2009.
PhD Thesis
- C. Cartis. On Interior Point Methods for Linear Programming, DAMTP, University of Cambridge, 2005.
(available upon request)