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Coralia Cartis

Prof. Coralia Cartis

PhD Mathematics, University of Cambridge (2005)
Status
Academic Faculty

Professor in Numerical Optimization, Mathematical Institute

Tutorial Fellow in Mathematics, Balliol College

Contact form
http://people.maths.ox.ac.uk/cartis
+44 1865 273526
ORCID iD
https://orcid.org/0000-0002-0963-5550
Research groups
  • Numerical Analysis
  • Data Science

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent publications
Corrigendum to “Nonlinear matrix recovery using optimization on the Grassmann manifold” [Appl. Comput. Harmon. Anal. 62 (2023) 498–542, (S1063520322000859), (10.1016/j.acha.2022.11.001)]
Goyens, F Cartis, C Eftekhari, A Applied and Computational Harmonic Analysis volume 63 93- (01 Mar 2023)
Nonlinear matrix recovery using optimization on the Grassmann manifold
Goyens, F Cartis, C Eftekhari, A Applied and Computational Harmonic Analysis volume 62 498-542 (01 Jan 2023)
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)
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.
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