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Research Output 1977 2019

2019
1 Downloads (Pure)

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

Cartis, C., Gould, N. I. M. & Toint, P., 1 Oct 2019, (Accepted/In press) In : Optimization Methods and Software. to appear

Research output: Contribution to journalArticle

Function evaluation
Unconstrained Optimization
Adaptive algorithms
Nonlinear Optimization
Tensors
2 Downloads (Pure)
File
Rain
Weather forecasting
Costs
5 Downloads (Pure)

A note on using performance and data profiles for training algorithms

Porcelli, M. & Toint, P. L., 1 Jan 2019, In : ACM Transactions on Mathematical Software. 45, 2, a20.

Research output: Contribution to journalArticle

File
Training Algorithm
Derivatives
Derivative-free
Integer
Benchmarking
13 Downloads (Pure)

Bernstein Concentration Inequalities for Tensors via Einstein Products

Luo, Z., Qi, L. & Toint, P., 11 Feb 2019, Arxiv, 12 p.

Research output: Working paper

File
Bernstein Inequality
Concentration Inequalities
Albert Einstein
Tensors
Tensor
2 Downloads (Pure)

Complexity of partially separable convexly constrained optimization with non-lipschitzian singularities

Chen, X., Toint, P. & Wang, H., 15 Apr 2019, In : SIAM Journal on Optimization. 29, 1, p. 874-903 30 p.

Research output: Contribution to journalArticle

Open Access
File
Constrained optimization
Constrained Optimization
Singularity
Objective function
Regularization

Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models

Cartis, C., Gould, N. I. M. & Toint, P., Jun 2019, Springer Optimization and Its Applications: Algorithms, Complexity and Applications. Demetriou, I. & Pardalos, P. (eds.). Springer Heidelberg, p. 5-26 22 p. (Springer Optimization and Its Applications; vol. 145).

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter

KKT Conditions
Constrained Optimization
Nonlinear Optimization
Higher Order
Derivatives
3 Downloads (Pure)

Exploiting variable precision in GMRES

Gratton, S., Simon, E., Titley-Peloquin, D. & Toint, P., Jul 2019, 19 p.

Research output: Working paper

File
GMRES
Digital arithmetic
Arnoldi
Iterative Solver
Floating-point Arithmetic
13 Downloads (Pure)
File
Constrained optimization
Constrained Optimization
Sparsity
Higher Order
Evaluation

In Memoriam of Andy Conn

Toint, P., 19 Nov 2019, In : SIAG/ OPT Views-and-News. 27, 2, p. 9-10 1 p.

Research output: Contribution to journalArticle

3 Downloads (Pure)
File
Derivatives
Evaluation
Adaptive algorithms
Nonconvex Minimization
Inexact Methods

Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization

Cartis, C., Gould, N. I. M. & Toint, P., 10 Aug 2019, In : Journal of Complexity. 53, p. 68-94 32 p.

Research output: Contribution to journalArticle

Open Access
File
Nonconvex Optimization
Constrained optimization
Constrained Optimization
Optimality
Criticality
1 Downloads (Pure)

Universal regularization methods: varying the power, the smoothness and the accuracy

Cartis, C., Gould, N. I. & Toint, P. L., 1 Jan 2019, In : SIAM Journal on Optimization. 29, 1, p. 595-615 21 p.

Research output: Contribution to journalArticle

Open Access
File
Regularization Method
Smoothness
Convergence of Algorithms
Trust Region
Nonconvex Optimization
2018
6 Downloads (Pure)

A note on preconditioning weighted linear least-squares with consequences for weakly constrained variational data assimilation

Gratton, S., Selime, G., Simon, E. & Toint, P., Apr 2018, In : Quarterly Journal of the Royal Meteorological Society. 144, 712, p. 934-940 7 p.

Research output: Contribution to journalArticle

File
Data Assimilation
Linear Least Squares
Weighted Least Squares
Preconditioning
data assimilation
1 Downloads (Pure)

A note on solving nonlinear optimization problems in variable precision

Gratton, S. & Toint, P., 11 Dec 2018, Arxiv, 11 p.

Research output: Working paper

File
Function evaluation
Energy dissipation
Costs
Experiments
data assimilation
erratic
matrix
method
12 Downloads (Pure)

Michael James David Powell: 29 July 1936-19 April 2015

Buhmann, M., Fletcher, R., Iserles, A. & Toint, P., 2018, In : Biogr. Mems Fell R. Soc. (London). 64: 341-366, 39 p.

Research output: Contribution to journalArticle

Open Access
File
11 Downloads (Pure)

Minimizing convex quadratics with variable precision Krylov methods

Gratton, S., Simon, E. & Toint, P., 2018, (Submitted) Arxiv, 26 p.

Research output: Working paper

File
Krylov Methods
Quadratic Optimization
Cross product
Matrix Product
Conjugate Gradient

Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization

Cartis, C., Gould, N. I. M. & Toint, P., 1 Oct 2018, In : Foundations of Computational Mathematics. 18, 5, p. 1073-1107 35 p.

Research output: Contribution to journalArticle

Constrained Optimization
Nonlinear Optimization
Optimality
Derivatives
Critical point
2 Downloads (Pure)
File
Derivatives
Costs
2017
5 Downloads (Pure)

An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

Curtis, F., Gould, N. I. M., Robinson, D. & Toint, P., Jan 2017, In : Mathematical Programming. 161, 1-2, p. 73-134 62 p.

Research output: Contribution to journalArticle

File
Interior Point
Nonlinear Optimization
Global Convergence
Matrix Derivative
Iteration
7 Downloads (Pure)
File
Direct Search
Derivative-free
Discrete Variables
Constrained optimization
Continuous Variables

On the complexity of finding first-order critical points in constrained nonlinear optimization: Corrigendum

Cartis, C., Gould, N. I. M. & Toint, P. L., 1 Jan 2017, In : Mathematical Programming. 161, 1-2, p. 611-626 16 p.

Research output: Contribution to journalArticle

Constrained Optimization
Nonlinear Optimization
Critical point
First-order
Constrained optimization
2 Downloads (Pure)

On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Gratton, S., Gürol, S., Simon, E. & Toint, P., 20 Sep 2017, (Submitted) Arxiv.

Research output: Working paper

File
Data Assimilation
Saddle
Parallel processing systems
data assimilation
parallel computing
26 Downloads (Pure)

Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization

Cartis, C., Gould, N. I. M. & Toint, P., 22 Sep 2017, Arxiv, 35 p.

Research output: Working paper

File
Newton-Raphson method
Optimality
Optimization
Function evaluation
Evaluation

Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Birgin, E. G., Gardenghi, J. L., Martínez, J. M., Santos, S. A. & Toint, P. L., 15 Apr 2017, In : Mathematical Programming. 163, 1-2, p. 359-368 10 p.

Research output: Contribution to journalArticle

Unconstrained Optimization
Nonlinear Optimization
Higher Order
Derivatives
Derivative
3 Downloads (Pure)
Open Access
File
Unconstrained Optimization
Regularization Method
Regularization
Gradient
Evaluation
2016
4 Downloads (Pure)

Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models

Birgin, E., Gardenghi, J., Martinez, J-M., Santos, S. & Toint, P., 2016, In : SIAM Journal on Optimization. 26, 2, 20 p.

Research output: Contribution to journalArticle

File
KKT Conditions
Constrained optimization
Constrained Optimization
Nonlinear Optimization
Higher Order
8 Downloads (Pure)
Open Access
File
Derivative-free
Nonlinear Constraints
Nonlinear Optimization
Nonlinear Problem
Derivative-free Optimization

Simple examples for the failure of Newton’s method with line search for strictly convex minimization

Jarre, F. & Toint, P. L., Jun 2016, In : Mathematical Programming. 158, 1, p. 23-34

Research output: Contribution to journalArticle

Convex Minimization
Line Search
Strictly Convex
Newton-Raphson method
Newton Methods
2015
Derivative-free
Constrained Optimization
Nonlinear Optimization
Interpolation
Equality

An interior-point ℓ1-penalty method for nonlinear optimization

Gould, N. I. M., Orban, D. & Toint, P. L., 2015, Springer Proceedings in Mathematics and Statistics: Proceedings of NAOIII 2014. Springer New York, Vol. 134. p. 117-150 34 p.

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)

Penalty Method
Interior Point
Nonlinear Optimization
Penalty
Penalty Function
62 Downloads (Pure)
File
Belgium
Belgian
simulation
municipality
travel
101 Downloads (Pure)

CUTEST: a Constrained and Unconstrained Testing Environment with safe threads

Gould, N. I. M., Orban, D. & Toint, P., 2015, In : Computational Optimization and Applications. 60, 3, p. 545-557 13 p.

Research output: Contribution to journalArticle

File
Storage allocation (computer)
Modular Design
Thread
MATLAB
Testing
24 Downloads (Pure)

Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models

Cartis, C., Gould, N. I. M. & Toint, P., 18 Nov 2015, 18 p. (naXys technical report).

Research output: Working paper

File
Euclidean norm
Local Minimizer
Vector-valued Functions
Taylor series
Criticality

Le théorème d'Alaoglu et ses suites

Toint, P., 2015, Géodésiques : Dix rencontres entre sciences et littérature. Godin, M. & Lambiotte, R. (eds.). L'arbre de Diane, p. 44-45 (La tortue de Zénon; no. 3).

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)

53 Downloads (Pure)

Observations Thinning In Data Assimilation Computations

Gratton, S., Rincon-Camacho, M., Simon, E. & Toint, P., 2015, In : EURO Journal on Computational Optimization. 3, p. 31-51

Research output: Contribution to journalArticle

File
Data Assimilation
Thinning
data assimilation
thinning
decomposition
35 Downloads (Pure)
Open Access
File
Constrained Least Squares
Nonlinear Least Squares
Constrained Optimization
Nonlinear Optimization
Nonconvex Optimization
10 Downloads (Pure)

Quasi-Newton updates with weighted secant equations

Gratton, S., Malmedy, V. & Toint, P., 4 Jul 2015, In : Optimization Methods and Software. 30, 4, p. 748-755 8 p.

Research output: Contribution to journalArticle

File
Quasi-Newton
Chord or secant line
Update
Sylvester Equation
10 Downloads (Pure)

Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Birgin, E., Gardenghi, J., Martinez, J-M., Santos, S. A. & Toint, P., Jun 2015, 2015: Namur center for complex systems, 8 p. (naXys Technical Reports; vol. 05-2015).

Research output: Working paper

File
Unconstrained Optimization
Nonlinear Optimization
Higher Order
Derivatives
Derivative
32 Downloads (Pure)

Worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization

Cartis, C., Rodrigues Sampaio, P. & Toint, P. L., 4 May 2015, In : Optimization. 64, 5, p. 1349-1361 13 p.

Research output: Contribution to journalArticle

File
Unconstrained Optimization
Gradient
Evaluation
Critical point
First-order
2014
116 Downloads (Pure)
File
Interior Point
Nonlinear Optimization
Matrix Derivative
Merit Function
Quadratic Optimization
43 Downloads (Pure)

Linearizing the Method of Conjugate Gradients

Gratton, S., Titley-Peloquin, D., Toint, P. & Tshimanga Ilunga, J., 2014, In : SIAM Journal on Matrix Analysis and Applications. 35, 1, p. 110-126

Research output: Contribution to journalArticle

Open Access
File
Jacobian matrices
Conjugate Gradient
Spectral Norm
Algorithm Design
Jacobian matrix
8 Downloads (Pure)

On the complexity of finding first-order critical points in constrained nonlinear optimization

Cartis, C., Gould, N. I. M. & Toint, P. L., 2014, In : Mathematical Programming. 144, 1-2, p. 93-106 14 p.

Research output: Contribution to journalArticle

File
Constrained Optimization
Nonlinear Optimization
Critical point
First-order
Optimization
2013
12 Downloads (Pure)

Adaptive Observations And Multilevel Optimization In Data Assimilation

Gratton, S., Rincon-Camacho, M. & Toint, P., 2013, Namur: Namur center for complex systems, 18 p.

Research output: Working paper

File
data assimilation
decomposition
wave equation
weather
prediction
57 Downloads (Pure)

Aircraft fuselage sizing with multilevel optimization

Colson, B., Porcelli, M. & Toint, P., 3 May 2013, Namur center for complex systems.

Research output: Book/Report/JournalCommissioned report

File
Belgium
aircraft
mathematics
63 Downloads (Pure)
File
Unconstrained Minimization
Steepest Descent Method
Evaluation Function
Terminate
Iterate

An original synthetic population tool applied to Belgian case: VirtualBelgium

Cornelis, E., Hollaert, L., Barthelemy, J. & Toint, P., 5 Mar 2013, NTTS - Conferences on New Techniques and Technologies for Statistics - Proceedings: The meeting place for Research in Official Statistics. Brussels: EUROSTAT, p. 695 - 701 7 p.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

5 Downloads (Pure)

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

Cartis, C., Gould, N. I. M. & Toint, P. L., 1 Jun 2013, In : Optimization Methods and Software. 28, 3, p. 451-457 7 p.

Research output: Contribution to journalArticle

File
Chebyshev
Nonconvex Optimization
Nonconvex Problems
Resolve
Lower bound
11 Downloads (Pure)

Conjugate gradients versus multigrid solvers for diffusion-based correlation models in data assimilation

Gratton, S., Toint, P. L. & Tshimanga, J., 2013, In : Quarterly Journal of the Royal Meteorological Society. 139, 675, p. 1481-1487 7 p.

Research output: Contribution to journalArticle

Open Access
File
data assimilation
comparison
17 Downloads (Pure)

Entends-tu cette main

Translated title of the contribution: Do you hear that handToint, P., 16 Oct 2013, 1 p. L'Arbre à paroles.

Research output: Other contribution

Open Access
File