Publications
2026
Journal Articles
1.
Diouane, Y., Gollier, M. & Orban, D. A nonsmooth exact penalty method for equality-constrained optimization: Complexity and implementation. SIAM Journal on Optimization 36, 626–650 (2026).
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2.
Diouane, Y., Habiboullah, M. L. & Orban, D. Complexity of trust-region methods in the presence of unbounded Hessian approximations. Mathematical Programming v, p–q (2026) (Online first).
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3.
Diouane, Y., Habiboullah, M. L. & Orban, D. A proximal modified quasi-Newton method for nonsmooth regularized optimization. SIAM Journal on Optimization 56, 534–563 (2026).
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4.
Leconte, G. & Orban, D. Complexity of trust-region methods with unbounded Hessian approximations for smooth and nonsmooth optimization. Mathematical Programming v, p–q (2026) (Online first).
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5.
Gollier, M., Habiboullah, M. L., Leconte, G., Baraldi, R., De Marchi, A., Orban, D. & Diouane, Y. RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization. Journal of Open Source Software 11, 9344 (2026).
6.
Migot, T., Monnet, D., Orban, D. & Siqueira, A. S. JSOSolvers.jl: Unconstrained and bound-constrained optimization solvers. Journal of Open Source Software 11, 9467 (2026).
Technical Reports
1.
De Marchi, A. & Orban, D. Envelopt: Constrained Convex Composite Optimization. 1–24 (2026).
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2025
Journal Articles
1.
Montoison, A., Orban, D. & Saunders, M. A. MINARES: An iterative solver for symmetric linear systems. SIAM Journal on Matrix Analysis and Applications 46, 509–529 (2025).
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2.
Ma, D., Orban, D. & Saunders, M. A. Solving algorithm NCL’s subproblems: The need for interior methods. Vietnam J. Math. 53, 915–919 (2025).
Technical Reports
1.
Allaire, N., Le Digabel, S. & Orban, D. An Inexact Modified Quasi-Newton Method for Nonsmooth Regularized Optimization. 1–21 (2025) doi:10.13140/RG.2.2.32728.97288.
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2024
Journal Articles
1.
Aravkin, A. Y., Baraldi, R. & Orban, D. A Levenberg–Marquardt method for nonsmooth regularized least squares. SIAM Journal on Scientific Computing 46, A2557–A2581 (2024).
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2.
Dussault, J.-P., Migot, T. & Orban, D. Scalable adaptive cubic regularization methods. Mathematical Programming 207, 191–225 (2024).
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3.
Leconte, G. & Orban, D. The indefinite proximal gradient method. Computational Optimization and Applications v, 43 (2024) (Published online).
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[Preprint]
Proceedings
1.
Migot, T., Orban, D. & Siqueira, A. S. JSOSuite.jl: Solving continuous optimization problems with JuliaSmoothOptimizers. in Proceedings of the 2024 JuliaCon conferences vol. 6 161 (The Open Journal, 2024).
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[Preprint]
Technical Reports
1.
Fowkes, J., Lister, A., Montoison, A. & Orban, D. LibHSL: The Ultimate Collection for Large-Scale Scientific Computation. 1–5 (2024) doi:10.13140/RG.2.2.30649.54889.
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2.
Leconte, G. & Orban, D. An Interior-Point Trust-Region Method for Nonsmooth Regularized Bound-Constrained Optimization. 1–32 (2024) doi:10.13140/RG.2.2.18132.99201.
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3.
Huang, N., Dai, Y.-H., Orban, D. & Saunders, M. A. An Inexact Augmented Lagrangian Algorithm for Unsymmetric Saddle-Point Systems. 1–26 (2024) doi:10.13140/RG.2.2.17308.09602.
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4.
Diouane, Y., Gürol, S., Mouthal, O. & Orban, D. An Efficient Scaled Spectral Preconditioner for Sequences of Symmetric Positive Definite Linear Systems. (2024) doi:10.13140/RG.2.2.28678.38725.
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2023
Journal Articles
1.
Montoison, A. & Orban, D.
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Krylov.jl: A Julia basket of hand-picked Krylov methods. The Journal of Open Source Software 89, 5187 (2023).[Preprint]
2.
Na Huang, D. O., Yu-Hong Dai & Saunders, M. A. Properties of semi-conjugate gradient methods for solving unsymmetric positive definite linear systems. Optimization Methods and Software 38, 887–913 (2023).
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3.
Huang, N., Dai, Y.-H., Orban, D. & Saunders, M. A. On GSOR, the generalized successive overrelaxation method for double saddle-point problems. SIAM Journal on Scientific Computing 45, A2185–A2206 (2023).
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[Preprint]
Technical Reports
1.
Bigeon, J., Orban, D. & Raynaud, P. A Framework Around Limited-Memory Partitioned Quasi-Newton Methods. 1–27 https://www.gerad.ca/en/papers/G-2023-17 (2023).
2.
Raynaud, P., Orban, D. & Bigeon, J. Partially-Separable Loss to Parallellize Partitioned Neural Network Training. 1–11 https://www.gerad.ca/en/papers/G-2023-36 (2023).
3.
Raynaud, P., Orban, D. & Bigeon, J. PLSR1: A Limited-Memory Partitioned Quasi-Newton Optimizer for Partially-Separable Loss Functions. 1–8 https://www.gerad.ca/en/papers/G-2023-41 (2023).
2022
Journal Articles
1.
Aravkin, A. Y., Baraldi, R. & Orban, D. A proximal quasi-Newton trust-region method for nonsmooth regularized optimization. SIAM Journal on Optimization 32, 900–929 (2022).
[Preprint]
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2.
Migot, T., Orban, D. & Soares Siqueira, A. DCISolver.jl: A Julia Solver for Nonlinear Optimization using Dynamic Control of Infeasibility. The Journal of Open Source Software 70, 3991 (2022).
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3.
Montoison, A. & Orban, D. GPMR: An iterative method for unsymmetric partitioned linear systems. SIAM Journal on Matrix Analysis 44, 293–311 (2022).
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4.
Migot, T., Orban, D. & Siqueira, A. S. PDENLPModels.jl: An NLPModel API for optimization problems with PDE constraints. Journal of Open Source Software 7, 4736 (2022).
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Technical Reports
1.
Orban, D. Computing a Sparse Projection into a Box. 1–15 (2022) doi:10.13140/RG.2.2.15115.98088.
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2.
Lakhmiri, Dounia, Orban, D. & Lodi, A. A Stochastic Proximal Method for Nonsmooth Regularized Finite Sum Optimization. 1–17 (2022) doi:10.48550/arXiv.2206.06531.
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2021
Journal Articles
1.
Serafino, D. di & Orban, D. Constraint-preconditioned Krylov solvers for regularized saddle-point systems. SIAM Journal on Scientific Computing 43, A1001–A1026 (2021).
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2.
Montoison, Alexis & Orban, D. TriCG and TriMR: Two iterative methods for symmetric quasi-definite systems. SIAM Journal on Scientific Computing 43, A2502–A2525 (2021).
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3.
Alexandre Ghannad, Orban, D. & Saunders, M. A. Linear systems arising in interior methods for convex optimization: A symmetric formulation with bounded condition number. Optimization Methods and Software 0, 1–26 (2021).
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[Preprint]
Proceedings
1.
Ma, D., Saunders, M. A. & Orban, D. A Julia implementation of algorithm NCL for constrained optimization. in Numerical analysis and optimization (eds. Al-Baali, M., Grandinetti, L. & Purnama, A.) vol. v p–q (Springer International Publishing, Switzerland, 2021). (special issue of NAOV, Muscat, Oman, 2017).
[Preprint]
[Preprint]
Technical Reports
1.
Leconte, G. & Orban, D. RipQP: A Multi-Precision Regularized Predictor-Corrector Method for Convex Quadratic Optimization. 1–34 https://www.gerad.ca/en/papers/G-2021-03 (2021).
2.
Aravkin, A., Baraldi, R., Leconte, G. & Orban, D. Corrigendum: A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization. 1–3 (2024) doi:10.13140/RG.2.2.36250.45768.
2020
Journal Articles
1.
Mestdagh, G., Goussard, Y. & Orban, D. Scaled projected-direction methods with application to transmission tomography. Optimization and Engineering 1–25 (2020) doi:10.1007/s11081-020-09484-0 (Online First).
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2.
R. Estrin, Friedlander, M. P., Orban, D. & Saunders, M. A. Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing 42, A1809–A1835 (2020).
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3.
R. Estrin, Friedlander, M. P., Orban, D. & Saunders, M. A. Implementing a smooth exact penalty function for general constrained nonlinear optimization. SIAM Journal on Scientific Computing 42, A1836–A1859 (2020).
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4.
Orban, D. & Siqueira, A. S. A regularization method for constrained nonlinear least squares. Computational Optimization and Applications 76, 961–989 (2020).
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5.
Montoison, A. & Orban, D. BiLQ: An iterative method for nonsymmetric linear systems with a quasi-minimum error property. SIAM Journal on Matrix Analysis and Applications 41, 1145–1166 (2020).
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Proceedings
1.
Lotfi, S., Bonniot de Ruisselet, T., Orban, D. & Lodi, A. Stochastic damped L-BFGS with controlled norm of the Hessian approximation. in (2020). doi:10.13140/RG.2.2.27851.41765/1 (OPT2020 Conference on Optimization for Machine Learning).
[Preprint]
[Preprint]
Technical Reports
1.
Lotfi, Sanae, Orban, D. & Lodi, A. Stochastic Adaptive Regularization with Dynamic Sampling for Machine Learning. 1–17 (2021).
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2019
Journal Articles
1.
M. Dehghani, A. Lambe & Orban, D. A regularized interior-point method for constrained linear least squares. INFOR: Information Systems and Operational Research 58, 202–224 (2019).
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2.
M.-A. Dahito & Orban, D. The conjugate residual method in linesearch and trust-region methods. SIAM Journal on Optimization 29, 1988–2025 (2019).
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3.
R. Estrin, Orban, D. & Saunders, M. A. Euclidean-norm error bounds for SYMMLQ and CG. SIAM Journal on Matrix Analysis 40, 235–253 (2019).
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4.
R. Estrin, Orban, D. & Saunders, M. A. LSLQ: An iterative method for linear least-squares with an error minimization property. SIAM Journal on Matrix Analysis 40, 254–275 (2019).
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5.
R. Estrin, Orban, D. & Saunders, M. A. LNLQ: An iterative method for least-norm problems with an error minimization property. SIAM Journal on Matrix Analysis 40, 1102–1124 (2019).
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6.
Buttari, A., Orban, D., Ruiz, D. & Titley-Peloquin, D. A tridiagonalization method for symmetric saddle-point system. SIAM Journal on Scientific Computing 41, S409–S432 (2019).
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2018
Journal Articles
1.
S. Arreckx & Orban, D. A regularized factorization-free method for equality-constrained optimization. SIAM Journal on Optimization 28, 1613–1639 (2018).
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Proceedings
1.
D. Ma, Judd, K., Orban, D. & Saunders, M. Stabilized optimization via an NCL algorithm. in Numerical analysis and optimization (eds. Al-Baali, M., Grandinetti, L. & Purnama, A.) vol. 235 173–191 (Springer International Publishing, Switzerland, 2018). (special issue of NAOIV, Muscat, Oman, 2017).
2017
Books
1.
Orban, D. & Arioli, M. Iterative Solution of Symmetric Quasi-Definite Linear Systems. vol. 3 (SIAM, 2017).
Technical Reports
1.
Côté, P., K. Demeester, Orban, D. & M. Towhidi. Numerical Methods for Stochastic Dynamic Programming with Application to Hydropower Optimization. (2017) doi:10.13140/RG.2.2.32660.81280.
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2.
Goussard, Y., M. McLaughlin & Orban, D. Factorization-Free Methods for Computed Tomography. (2017) doi:10.13140/RG.2.2.17141.88808.
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3.
A.-S. Crélot, Beauthier, C., Orban, D., Sainvitu, C. & Sartenaer, A. Combining Surrogate Strategies with MADS for Mixed-Variable Derivative-Free Optimization. (2017) doi:10.13140/RG.2.2.25690.24008.
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2016
Journal Articles
1.
A. Dehghani, Goffin, J.-L. & Orban, D. A primal-dual regularized interior-point method for semidefinite programming. Optimization Methods and Software 32, 193–219 (2017).
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Technical Reports
1.
S. Arreckx, Orban, D. & N. van Omme. NLP.py: An Object-Oriented Environment for Large-Scale Optimization. (2016) doi:10.13140/RG.2.1.2846.6803.
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2015
Books
1.
Guérin, J. & Orban, D. Analyse Pour Ingénieurs. (Publisher to be determined, 2016). (In preparation).
Journal Articles
1.
S. Arreckx, A. Lambe, Martins, J. R. R. A. & Orban, D. A matrix-free augmented Lagrangian algorithm with application to large-scale structural design optimization. Optimization and Engineering 17, 359–384 (2016) (Online First October 2015).
2.
Gould, N. I. M., Orban, D. & L. Toint, Ph. CUTEst: A Constrained and Unconstrained Testing Environment with safe threads for Mathematical Optimization. Computational Optimization and Applications 60, 545–557 (2015).
3.
Orban, D. Limited-memory \(LDL^T\) factorization of symmetric quasi-definite matrices with application to constrained optimization. Numerical Algorithms 70, 9–41 (2015).
4.
Orban, D. & M. Towhidi. Customizing the solution process of COIN-OR’s linear solvers with Python. Mathematical Programming Computation 8, 377–391 (2016) (Winner of the 2014 COIN-OR Cup).
Proceedings
1.
Gould, N. I. M., Orban, D. & L. Toint, Ph. An interior-point \(\ell_{1}\)-penalty method for nonlinear optimization. in Recent developments in numerical analysis and optimization (eds. Al-Baali, M., Grandinetti, L. & Purnama, A.) vol. 134 117–150 (Springer, Switzerland, 2015). (special issue of NAOIII, Muscat, Oman, 2014).
Technical Reports
Unpublished
1.
Orban, D. A Collection of Linear Systems Arising from Interior-Point Methods for Quadratic Optimization. (2015).
[Preprint]
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2014
Journal Articles
1.
Greif, C., E. Moulding & Orban, D. Bounds on the eigenvalues of matrices arising from interior-point methods. SIAM Journal on Optimization 24, 49–83 (2014).
2.
Audet, C., C.-K. Dang & Orban, D. Optimization of algorithms with OPAL. Mathematical Programming Computation 6, 233–254 (2014).
3.
Gould, N. I. M., Orban, D. & Rees, T. Projected Krylov methods for saddle-point systems. SIAM Journal on Matrix Analysis and Applications 35, 1329–1343 (2014).
Technical Reports
1.
Orban, D. The Projected Golub-Kahan Process for Constrained Linear Least-Squares Problems. (2014).
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2013
Journal Articles
1.
Gould, N. I. M., Orban, D. & D. Robinson. Trajectory-following methods for large-scale degenerate convex quadratic programming. Mathematical Programming Computation 5, 113–142 (2013).
2.
J.-P. Harvey, Chartrand, P., Eriksson, G. & Orban, D. Global minimization of the Gibbs energy of multicomponent systems involving the presence of order/disorder phase transitions. American Journal of Science 313, 199–241 (2013).
2012
Journal Articles
1.
Armand, P., Benoist, J. & Orban, D. From global to local convergence of interior methods for nonlinear optimization. Optimization Methods and Software 28, 1051–1080 (2012).
2.
Friedlander, M. P. & Orban, D. A primal-dual regularized interior-point method for convex quadratic programs. Mathematical Programming Computation 4, 71–107 (2012).
3.
Z. Coulibaly & Orban, D. An \(\ell_1\) elastic interior-point method for mathematical programs with complementarity constraints. SIAM Journal on Optimization 22, 187–211 (2012).
4.
Armand, P. & Orban, D. The squared slacks transformation in nonlinear programming. Sultan Qaboos University Journal for Science 17, 22–29 (2012).
Technical Reports
1.
Dehghani, A., Goffin, J.-L. & Orban, D. Solving Unconstrained Nonlinear Programs Using ACCPM. (2012).
[Preprint]
[Preprint]
Unpublished
1.
Orban, D. Numerical optimization in the Python ecosystem. (2013).
2011
Journal Articles
1.
Audet, C., C.-K. Dang & Orban, D. Efficient use of parallelism in algorithmic parameter optimization applications. Optimization Letters 7, 421–433 (2011).
Unpublished
1.
2.
Ayotte-Sauvé, E., M. Chugunova, Cortes, B., Lina, A., A. Majumdar, Orban, D., C. Prior & Zalzal, V. On Equidistant Points on a Curve. (2011) (Fourth industrial problem solving workshop).
2010
Journal Articles
1.
Orban, D., V. Raymond & Soumis, F. A new version of the improved primal simplex for degenerate linear programs. Computers and Operations Research 37, 91–98 (2010).
2.
Fourer, R., Maheshwari, C., Neumaier, A., Orban, D. & Schichl, H. Convexity and concavity detection in computational graphs. INFORMS Journal on Computing 22, 26–43 (2010).
3.
Fourer, R. & Orban, D. The DrAMPL meta solver for optimization problem analysis. Computational Management Science 7, 437–463 (2010) (Winner of the Computational Management Science 2010 Best Paper Prize).
Proceedings
1.
Audet, C., C.-K. Dang & Orban, D. Algorithmic parameter optimization of the DFO method with the OPAL framework. in Software automatic tuning: From concepts to state-of-the-art results (eds. Naono, K., Teranishi, K., Cavazos, J. & Suda, R.) 255–274 (Springer, New-York, NY, 2010). doi:10.1007/978-1-4419-6935-4.
2.
J.-P. Harvey, Chartrand, P., Eriksson, G. & Orban, D. Gibbs energy minimization challenges using implicit variables solution models. in TOFA: Discussion meeting on thermodynamics of alloys (2010).
2009
Journal Articles
1.
Armand, P., A. Kiselev, Marcotte, O. & Orban, D. Self calibration of a pinhole camera. Mathematics-in-Industry Case Studies 1, 81–98 (2009).
Unpublished
1.
2008
Journal Articles
1.
Armand, P., Benoist, J. & Orban, D. Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming. Computational Optimization and Applications 41, 1–25 (2008).
Unpublished
1.
Gould, N. I. M., Orban, D. & L. Toint, Ph. LANCELOT_SIMPLE: A Simple Interface for LANCELOT-b. (2008).
[Preprint]
[Preprint]
2.
2006
Journal Articles
1.
Audet, C. & Orban, D. Finding optimal algorithmic parameters using the mesh adaptive direct search algorithm. SIAM Journal on Optimization 17, 642–664 (2006).
2.
Waltz, R. A., Morales, J. L., Nocedal, J. & Orban, D. An interior algorithm for nonlinear optimization that combines line search and trust region steps. Mathematical Programming 107, 391–408 (2006).
[Preprint]
[Preprint]
2005
Journal Articles
1.
Gould, N., Orban, D. & Toint, P. Numerical methods for large-scale nonlinear optimization. Acta Numerica 14, 299–361 (2005).
2.
Gould, N. I. M., Orban, D., Sartenaer, A. & Toint, P. L. Sensitivity of trust-region algorithms to their parameters. 4OR 3, 227–241 (2005).
Proceedings
1.
Menvielle, N., Goussard, Y., Orban, D. & Soulez, G. Reduction of beam-hardening artifacts in X-ray CT. in Engineering in medicine and biology society, 2005. 27th annual international conference of the IEEE-EMBS 2005. 1865–1868 (2005). doi:10.1109/IEMBS.2005.1616814.
2003
Journal Articles
1.
Gould, N. I. M., Orban, D. & Toint, Ph. L. CUTEr and SifDec: A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 373–394 (2003).
[Preprint]
[Preprint]
2.
Gould, N. I. M., Orban, D. & Toint, Ph. L. GALAHAD, a library of thread-safe fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29, 353–372 (2003).
2002
Journal Articles
1.
Gould, N. I. M., Orban, D., Sartenaer, A. & Toint, P. L. Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Mathematical Programming 92, 481–508 (2002).
[Preprint]
[Preprint]
2.
Wright, S. J. & Orban, D. Properties of the log-barrier function on degenerate nonlinear programs. Mathematics of Operations Research 27, 585–613 (2002).
[Preprint]
[Preprint]
Unpublished
1.
Gould, N. I. M., Orban, D. & L. Toint, Ph. Results from a Numerical Evaluation of LANCELOT b. (2002).
[Preprint]
[Preprint]
2001
Journal Articles
1.
Gould, N. I. M., Orban, D., Sartenaer, A. & L. Toint, Philippe. Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM Journal on Optimization 11, 974–1002 (2001).
2000
Journal Articles
1.
Conn, A. R., Gould, N. I. M., Orban, D. & Toint, P. L. A primal-dual trust-region algorithm for non-convex nonlinear programming. Mathematical Programming 87, 215–249 (2000).