Publications

• Optimal Newton-type methods for nonconvex smooth optimization problems
• Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results
• A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
• Compressed sensing: how sharp is the restricted isometry property?
• Phase transitions for greedy sparse approximation algorithms
• On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
• On the complexity of finding first-order critical points in constrained nonlinear programming
• Complexity bounds for second-order optimality in unconstrained optimization
• Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity
• Convergence of a Regularized Euclidean Residual algorithm for nonlinear least-squares
• On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization
• On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
• Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
• Decay properties of restricted isometry constants
• Some disadvantages of a Mehrotra-type primal-dual corrector interior point algorithm for linear programming
• Trust-region and other regularisations of linear least-squares problems
• An adaptive cubic regularisation algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
• A new perspective on the complexity of interior point methods for linear programming
• Finding a point in the relative interior of a polyhedron
• On the convergence of a primal-dual second-order corrector interior point algorithm for linear programming
• Some new results concerning the primal-dual path-following interior point algorithm for linear programming

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Optimal Newton-type methods for nonconvex smooth optimization problems (2011)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 11-009, School of Mathematics, University of Edinburgh
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-11-009.html

Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results (2011)

C Cartis, N I M Gould and Ph L Toint
Mathematical Programming, vol: 127(2)
Page: 245-295
DOI: 10.1007/s10107-009-0286-5

A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function (2011)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 11-013, School of Mathematics, University of Edinburgh.
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-11-013.html

Compressed sensing: how sharp is the restricted isometry property? (2011)

J D Blanchard, C Cartis and J Tanner
SIAM Review, vol: 53(1)
Page: 105-125

Phase transitions for greedy sparse approximation algorithms (2011)

J D Blanchard, C Cartis, J Tanner and A Thompson
Applied and Computational Harmonic Analysis (ACHA), vol: 30
Page: 188-203

On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming (2011)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 11-002, School of Mathematics, University of Edinburgh
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-11-002.html

On the complexity of finding first-order critical points in constrained nonlinear programming (2011)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 11-005, School of Mathematics, University of Edinburgh
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-11-005.html

Complexity bounds for second-order optimality in unconstrained optimization (2011)

C Cartis, N I M Gould and Ph L Toint
Output type: Journal of Complexity (2011)
DOI / Link: 10.1016/j.jco.2011.06.001

Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity (2010, online)

C Cartis, N I M Gould and Ph L Toint
Mathematical Programming
Page: 25 pages
DOI / Link: 10.1007/s10107-009-0337-y

Convergence of a Regularized Euclidean Residual algorithm for nonlinear least-squares (2010)

S Bellavia, C Cartis, N I M Gould, B Morini, Ph L Toint
SIAM Journal on Numerical Analysis, vol: 48(1)
Page: 1--29

On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization (2010)

C Cartis, N I M Gould and Ph L Toint
SIAM Journal on Optimization, vol: 20(6)
Status: online
Page: 2833–2852

On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization (2010)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 10-005
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-10-005.html

Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization (2010)

C Cartis, N I M Gould and Ph L Toint
Output type: ERGO Technical Report 10-006, School of Mathematics, University of Edinburgh. To appear in Optimization Methods and Software, 2011.
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-10-006.html

Decay properties of restricted isometry constants (2009)

J D Blanchard, C Cartis and J Tanner
IEEE Signal Processing Letters, vol: 16(7)
Page: 572--575

Some disadvantages of a Mehrotra-type primal-dual corrector interior point algorithm for linear programming (2009)

C Cartis
Applied Numerical Mathematics, vol: 59
Page: 1110--1119

Trust-region and other regularisations of linear least-squares problems (2009)

C Cartis, N I M Gould and Ph L Toint
BIT, vol: 49(1)
Page: 21--53

An adaptive cubic regularisation algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity (2009)

C Cartis, N I M Gould and Ph L Toint
Output type: To appear in the IMA Journal of Numerical Analysis, 2011
DOI / Link: http://www.maths.ed.ac.uk/ERGO/pubs/ERGO-09-004.html

A new perspective on the complexity of interior point methods for linear programming (2007)

C Cartis and R Hauser
DOI / Link: http://web2.comlab.ox.ac.uk/oucl/publications/natr/NA-07-05.html

Finding a point in the relative interior of a polyhedron (2006)

C Cartis and N I M Gould
DOI / Link: http://www.optimization-online.org/DB_HTML/2006/12/1552.html

On the convergence of a primal-dual second-order corrector interior point algorithm for linear programming (2005)

C Cartis
DOI / Link: http://www.optimization-online.org/DB_HTML/2005/03/1097.html

Some new results concerning the primal-dual path-following interior point algorithm for linear programming (2005)

C Cartis
DOI / Link: http://web2.comlab.ox.ac.uk/oucl/publications/natr/na-05-06.html

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