# Prof. Coralia Cartis

PhD Mathematics, University of Cambridge (2005)

Status

Academic Faculty

Professor in Numerical Optimization, Mathematical Institute

Tutorial Fellow in Mathematics, Balliol College

Research groups

**Address**

Mathematical Institute

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

Recent publications

Scalable subspace methods for derivative-free nonlinear least-squares optimization

*Cartis, C*

*Roberts, L*

*MATHEMATICAL PROGRAMMING*

*(09 Jun 2022)*

Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings

*Cartis, C*

*Massart, E*

*Otemissov, A*

*MATHEMATICAL PROGRAMMING*

*(14 May 2022)*

A derivative-free optimisation method for global ocean biogeochemical models

*Oliver, S*

*Cartis, C*

*Kriest, I*

*Tett, S*

*Khatiwala, S*

*Geoscientific Model Development*

*volume 15*

*issue 9*

*3537-3554*

*(05 May 2022)*

Does model calibration reduce uncertainty in climate projections?

*Cartis, C*

*Journal of Climate*

*volume 35*

*issue 8*

*2585-2602*

*(13 Jan 2022)*

A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality

*Cartis, C*

*Otemissov, A*

*Information and Inference: a Journal of the IMA*

*volume 11*

*issue 1*

*167-201*

*(19 May 2021)*

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.