## Status:

Associate Professor in Numerical Optimization, Mathematical Institute

Tutorial Fellow in Mathematics, Balliol College

## Personal website:

## 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:

Adaptive regularization with cubics on manifolds

Mathematical Programming
(13 May 2020)

Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

SIAM Journal on Optimization
volume abs/1811.01220
(2020)

On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces

BIT Numerical Mathematics
(13 December 2019)

A concise second-order complexity analysis for unconstrained optimization using high-order regularized models

OPTIMIZATION METHODS & SOFTWARE
page 1-14
(26 October 2019)
Full text available

Improving the flexibility and robustness of model-based derivative-free optimization solvers

ACM Transactions on Mathematical Software
issue 3
volume 45
page 32:1-32:1
(12 August 2019)

## 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.