Publications

2024

Journal Articles

Aravkin, A. Y., Baraldi, R., & Orban, D. (2024). A Levenberg–Marquardt method for nonsmooth regularized least squares. SIAM Journal on Scientific Computing, 46(4), A2557–A2581. https://doi.org/10.1137/22M1538971

Dussault, J.-P., Migot, T., & Orban, D. (2024). Scalable adaptive cubic regularization methods. Mathematical Programming, 207, 191–225. https://doi.org/10.1007/s10107-023-02007-6

Proceedings

Migot, T., Orban, D., & Siqueira, A. S. (2024). JSOSuite.jl: Solving continuous optimization problems with JuliaSmoothOptimizers. Proceedings of the 2024 JuliaCon Conferences, 6, 161. https://doi.org/10.21105/jcon.00161

Technical Reports

Diouane, Y., Gollier, M., & Orban, D. (2024). A nonsmooth exact penalty method for equality-constrained optimization: Complexity and implementation (Cahier Du GERAD G-2024-65). GERAD. https://doi.org/10.13140/RG.2.2.16095.47527

Diouane, Y., Gürol, S., Mouthal, O., & Orban, D. (2024). An efficient scaled spectral preconditioner for sequences of symmetric positive definite linear systems (Cahier Du GERAD G-2024-66). GERAD. https://doi.org/10.13140/RG.2.2.28678.38725

Diouane, Y., Habiboullah, M. L., & Orban, D. (2024). A proximal modified quasi-Newton method for nonsmooth regularized optimization (Cahier Du GERAD G-2024-64). GERAD. https://doi.org/10.13140/RG.2.2.21140.51840

Diouane, Y., Habiboullah, M. L., & Orban, D. (2024). Complexity of trust-region methods in the presence of unbounded Hessian approximations (Cahier Du GERAD G-2024-43; pp. 1–18). GERAD. https://doi.org/10.48550/arXiv.2408.06243

Fowkes, J., Lister, A., Montoison, A., & Orban, D. (2024). LibHSL: The ultimate collection for large-scale scientific computation (Cahier Du GERAD G-2024-06; pp. 1–5). GERAD. https://doi.org/10.13140/RG.2.2.30649.54889

Huang, N., Dai, Y.-H., Orban, D., & Saunders, M. A. (2024). An inexact augmented Lagrangian algorithm for unsymmetric saddle-point systems (Cahier Du GERAD G-2024-30; pp. 1–26). GERAD. https://doi.org/10.13140/RG.2.2.17308.09602

Leconte, G., & Orban, D. (2024). An interior-point trust-region method for nonsmooth regularized bound-constrained optimization (Cahier Du GERAD G-2024-17; pp. 1–32). GERAD. https://doi.org/10.13140/RG.2.2.18132.99201

2023

Journal Articles

Huang, N., Dai, Y.-H., Orban, D., & Saunders, M. A. (2023). On GSOR, the generalized successive overrelaxation method for double saddle-point problems. SIAM Journal on Scientific Computing, 45(5), A2185–A2206. https://doi.org/10.1137/22M1515884

Montoison, A., & Orban, D. (2023). Krylov.jl: A Julia basket of hand-picked Krylov methods. The Journal of Open Source Software, 89(8), 5187. https://doi.org/10.21105/joss.05187

Technical Reports

Bigeon, J., Orban, D., & Raynaud, P. (2023). A framework around limited-memory partitioned quasi-Newton methods (Cahier Du GERAD G-2023-17; pp. 1–27). GERAD. https://www.gerad.ca/en/papers/G-2023-17

Leconte, G., & Orban, D. (2023). Complexity of trust-region methods with unbounded Hessian approximations for smooth and nonsmooth optimization (Cahier Du GERAD G-2023-65; pp. 1–18). GERAD. https://doi.org/10.13140/RG.2.2.22451.40486

Leconte, G., & Orban, D. (2023). The indefinite proximal gradient method (Cahier Du GERAD G-2023-37; pp. 1–24). GERAD. https://doi.org/10.13140/RG.2.2.11836.41606

Montoison, A., Orban, D., & Saunders, M. A. (2023). MINARES: An iterative solver for symmetric linear systems (Cahier Du GERAD G-2023-40; pp. 1–18). GERAD. https://doi.org/10.13140/RG.2.2.18163.91683

Raynaud, P., Orban, D., & Bigeon, J. (2023). Partially-separable loss to parallellize partitioned neural network training (Cahier Du GERAD G-2023-36; pp. 1–11). GERAD. https://www.gerad.ca/en/papers/G-2023-36

Raynaud, P., Orban, D., & Bigeon, J. (2023). PLSR1: A limited-memory partitioned quasi-Newton optimizer for partially-separable loss functions (Cahier Du GERAD G-2023-41; pp. 1–8). GERAD. https://www.gerad.ca/en/papers/G-2023-41

2022

Journal Articles

Aravkin, A. Y., Baraldi, R., & Orban, D. (2022). A proximal quasi-Newton trust-region method for nonsmooth regularized optimization. SIAM Journal on Optimization, 32(2), 900–929. https://doi.org/10.1137/21M1409536

Migot, T., Orban, D., & Siqueira, A. S. (2022). PDENLPModels.jl: An NLPModel API for optimization problems with PDE constraints. Journal of Open Source Software, 7(80), 4736. https://doi.org/10.21105/joss.04736

Migot, T., Orban, D., & Soares Siqueira, A. (2022). DCISolver.jl: A Julia Solver for Nonlinear Optimization using Dynamic Control of Infeasibility. The Journal of Open Source Software, 70(7), 3991. https://doi.org/10.21105/joss.03991

Montoison, A., & Orban, D. (2022). GPMR: An iterative method for unsymmetric partitioned linear systems. SIAM Journal on Matrix Analysis, 44(1), 293–311. https://doi.org/10.1137/21M1459265

Technical Reports

Lakhmiri, Dounia, Orban, D., & Lodi, A. (2022). A stochastic proximal method for nonsmooth regularized finite sum optimization (Cahier Du GERAD G-2022-27; pp. 1–17). GERAD. https://doi.org/10.48550/arXiv.2206.06531

Orban, D. (2022). Computing a sparse projection into a box (Cahier Du GERAD G-2022-12; pp. 1–15). GERAD. https://doi.org/10.13140/RG.2.2.15115.98088

2021

Journal Articles

Alexandre Ghannad, Orban, D., & Saunders, M. A. (2021). Linear systems arising in interior methods for convex optimization: A symmetric formulation with bounded condition number. Optimization Methods and Software, 0(0), 1–26. https://doi.org/10.1080/10556788.2021.1965599

Montoison, Alexis, & Orban, D. (2021). TriCG and TriMR: Two iterative methods for symmetric quasi-definite systems. SIAM Journal on Scientific Computing, 43(4), A2502–A2525. https://doi.org/10.1137/20M1363030

Serafino, D. di, & Orban, D. (2021). Constraint-preconditioned Krylov solvers for regularized saddle-point systems. SIAM Journal on Scientific Computing, 43(2), A1001–A1026. https://doi.org/10.1137/19M1291753

Proceedings

Ma, D., Saunders, M. A., & Orban, D. (2021). A Julia implementation of algorithm NCL for constrained optimization. In M. Al-Baali, L. Grandinetti, & A. Purnama (Eds.), Numerical analysis and optimization: Vol. v (pp. p–q). Springer International Publishing.

Technical Reports

Aravkin, A., Baraldi, R., Leconte, G., & Orban, D. (2024). Corrigendum: A proximal quasi-Newton trust-region method for nonsmooth regularized optimization (Cahier Du GERAD G-2021-12-SM; pp. 1–3). GERAD. https://doi.org/10.13140/RG.2.2.36250.45768

Leconte, G., & Orban, D. (2021). RipQP: A multi-precision regularized predictor-corrector method for convex quadratic optimization (Cahier Du GERAD G-2021-03; pp. 1–34). GERAD. https://www.gerad.ca/en/papers/G-2021-03

2020

Journal Articles

Mestdagh, G., Goussard, Y., & Orban, D. (2020). Scaled projected-direction methods with application to transmission tomography. Optimization and Engineering, 1–25. https://doi.org/10.1007/s11081-020-09484-0

Montoison, A., & Orban, D. (2020). BiLQ: An iterative method for nonsymmetric linear systems with a quasi-minimum error property. SIAM Journal on Matrix Analysis and Applications, 41(3), 1145–1166. https://doi.org/10.1137/19M1290991

Orban, D., & Siqueira, A. S. (2020). A regularization method for constrained nonlinear least squares. Computational Optimization and Applications, 76, 961–989. https://doi.org/10.1007/s10589-020-00201-2

R. Estrin, Friedlander, M. P., Orban, D., & Saunders, M. A. (2020). Implementing a smooth exact penalty function for equality-constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1809–A1835. https://doi.org/10.1137/19M1238265

R. Estrin, Friedlander, M. P., Orban, D., & Saunders, M. A. (2020). Implementing a smooth exact penalty function for general constrained nonlinear optimization. SIAM Journal on Scientific Computing, 42(3), A1836–A1859. https://doi.org/10.1137/19M1255069

Proceedings

Lotfi, S., Bonniot de Ruisselet, T., Orban, D., & Lodi, A. (2020). Stochastic damped L-BFGS with controlled norm of the Hessian approximation. https://doi.org/10.13140/RG.2.2.27851.41765/1

Technical Reports

Lotfi, Sanae, Orban, D., & Lodi, A. (2021). Stochastic adaptive regularization with dynamic sampling for machine learning (Cahier Du GERAD G-2020-51; pp. 1–17). GERAD.

2019

Journal Articles

Buttari, A., Orban, D., Ruiz, D., & Titley-Peloquin, D. (2019). A tridiagonalization method for symmetric saddle-point system. SIAM Journal on Scientific Computing, 41(5), S409–S432. https://doi.org/10.1137/18M1194900

M. Dehghani, A. Lambe, & Orban, D. (2019). A regularized interior-point method for constrained linear least squares. INFOR: Information Systems and Operational Research, 58(2), 202–224. https://doi.org/10.1080/03155986.2018.1559428

M.-A. Dahito, & Orban, D. (2019). The conjugate residual method in linesearch and trust-region methods. SIAM Journal on Optimization, 29(3), 1988–2025. https://doi.org/10.1137/18M1204255

R. Estrin, Orban, D., & Saunders, M. A. (2019). Euclidean-norm error bounds for SYMMLQ and CG. SIAM Journal on Matrix Analysis, 40(1), 235–253. https://doi.org/10.1137/16M1094816

R. Estrin, Orban, D., & Saunders, M. A. (2019). LNLQ: An iterative method for least-norm problems with an error minimization property. SIAM Journal on Matrix Analysis, 40(3), 1102–1124. https://doi.org/10.1137/18M1194948

R. Estrin, Orban, D., & Saunders, M. A. (2019). LSLQ: An iterative method for linear least-squares with an error minimization property. SIAM Journal on Matrix Analysis, 40(1), 254–275. https://doi.org/10.1137/17M1113552

2018

Journal Articles

S. Arreckx, & Orban, D. (2018). A regularized factorization-free method for equality-constrained optimization. SIAM Journal on Optimization, 28(2), 1613–1639. https://doi.org/10.1137/16M1088570

Proceedings

D. Ma, Judd, K., Orban, D., & Saunders, M. (2018). Stabilized optimization via an NCL algorithm. In M. Al-Baali, L. Grandinetti, & A. Purnama (Eds.), Numerical analysis and optimization (Vol. 235, pp. 173–191). Springer International Publishing. https://doi.org/10.1007/978-3-319-90026-1\_8

2017

Books

Orban, D., & Arioli, M. (2017). Iterative solution of symmetric quasi-definite linear systems (Vol. 3). SIAM. https://doi.org/10.1137/1.9781611974737

Technical Reports

A.-S. Crélot, Beauthier, C., Orban, D., Sainvitu, C., & Sartenaer, A. (2017). Combining surrogate strategies with MADS for mixed-variable derivative-free optimization (Cahier Du GERAD G-2017-70). GERAD. https://doi.org/10.13140/RG.2.2.25690.24008

Côté, P., K. Demeester, Orban, D., & M. Towhidi. (2017). Numerical methods for stochastic dynamic programming with application to hydropower optimization (Cahier Du GERAD G-2017-64). GERAD. https://doi.org/10.13140/RG.2.2.32660.81280

Goussard, Y., M. McLaughlin, & Orban, D. (2017). Factorization-free methods for computed tomography (Cahier Du GERAD G-2017-65). GERAD. https://doi.org/10.13140/RG.2.2.17141.88808

2016

Journal Articles

A. Dehghani, Goffin, J.-L., & Orban, D. (2017). A primal-dual regularized interior-point method for semidefinite programming. Optimization Methods and Software, 32(1), 193–219. https://doi.org/10.1080/10556788.2016.1235708

Technical Reports

S. Arreckx, Orban, D., & N. van Omme. (2016). NLP.py: An object-oriented environment for large-scale optimization (Cahier Du GERAD G-2016-42). GERAD. https://doi.org/10.13140/RG.2.1.2846.6803

2015

Journal Articles

Orban, D., & M. Towhidi. (2016). Customizing the solution process of COIN-OR’s linear solvers with Python. Mathematical Programming Computation, 8(4), 377–391. https://doi.org/10.1007/s12532-015-0094-2

S. Arreckx, A. Lambe, Martins, J. R. R. A., & Orban, D. (2016). A matrix-free augmented Lagrangian algorithm with application to large-scale structural design optimization. Optimization and Engineering, 17, 359–384. https://doi.org/10.1007/s11081-015-9287-9

Gould, N. I. M., Orban, D., & L. Toint, Ph. (2015). CUTEst: A Constrained and Unconstrained Testing Environment with safe threads for Mathematical Optimization. Computational Optimization and Applications, 60, 545–557. https://doi.org/10.1007/s10589-014-9687-3

Orban, D. (2015). Limited-memory \(LDL^T\) factorization of symmetric quasi-definite matrices with application to constrained optimization. Numerical Algorithms, 70(1), 9–41. https://doi.org/10.1007/s11075-014-9933-x

Proceedings

Gould, N. I. M., Orban, D., & L. Toint, Ph. (2015). An interior-point \(\ell_{1}\)-penalty method for nonlinear optimization. In M. Al-Baali, L. Grandinetti, & A. Purnama (Eds.), Recent developments in numerical analysis and optimization (Vol. 134, pp. 117–150). Springer. https://doi.org/10.1007/978-3-319-17689-5

Unpublished

Orban, D. (2015). A collection of linear systems arising from interior-point methods for quadratic optimization (Cahier Du GERAD G-2015-117). GERAD.

2014

Journal Articles

Audet, C., C.-K. Dang, & Orban, D. (2014). Optimization of algorithms with OPAL. Mathematical Programming Computation, 6(3), 233–254. https://doi.org/10.1007/s12532-014-0067-x

Gould, N. I. M., Orban, D., & Rees, T. (2014). Projected Krylov methods for saddle-point systems. SIAM Journal on Matrix Analysis and Applications, 35(4), 1329–1343. https://doi.org/10.1137/130916394

Greif, C., E. Moulding, & Orban, D. (2014). Bounds on the eigenvalues of matrices arising from interior-point methods. SIAM Journal on Optimization, 24(1), 49–83. https://doi.org/10.1137/120890600

Technical Reports

Orban, D. (2014). The projected Golub-Kahan process for constrained linear least-squares problems (Cahier Du GERAD G-2014-15). GERAD.

2013

Journal Articles

Gould, N. I. M., Orban, D., & D. Robinson. (2013). Trajectory-following methods for large-scale degenerate convex quadratic programming. Mathematical Programming Computation, 5(2), 113–142. https://doi.org/10.1007/s12532-012-0050-3

J.-P. Harvey, Chartrand, P., Eriksson, G., & Orban, D. (2013). Global minimization of the Gibbs energy of multicomponent systems involving the presence of order/disorder phase transitions. American Journal of Science, 313, 199–241. https://doi.org/10.2475/03.2013.02

2012

Journal Articles

Armand, P., Benoist, J., & Orban, D. (2012). From global to local convergence of interior methods for nonlinear optimization. Optimization Methods and Software, 28(5), 1051–1080. https://doi.org/10.1080/10556788.2012.668905

Armand, P., & Orban, D. (2012). The squared slacks transformation in nonlinear programming. Sultan Qaboos University Journal for Science, 17(1), 22–29.

Friedlander, M. P., & Orban, D. (2012). A primal-dual regularized interior-point method for convex quadratic programs. Mathematical Programming Computation, 4(1), 71–107. https://doi.org/10.1007/s12532-012-0035-2

Z. Coulibaly, & Orban, D. (2012). An \(\ell_1\) elastic interior-point method for mathematical programs with complementarity constraints. SIAM Journal on Optimization, 22(1), 187–211. https://doi.org/10.1137/090777232

Technical Reports

Dehghani, A., Goffin, J.-L., & Orban, D. (2012). Solving unconstrained nonlinear programs using ACCPM (Cahier Du GERAD G-2012-02). GERAD.

Unpublished

Orban, D. (2013). Numerical optimization in the Python ecosystem. GERAD Newsletter.

2011

Journal Articles

Audet, C., C.-K. Dang, & Orban, D. (2011). Efficient use of parallelism in algorithmic parameter optimization applications. Optimization Letters, 7(3), 421–433. https://doi.org/10.1007/s11590-011-0428-6

Unpublished

Ayotte-Sauvé, E., M. Chugunova, Cortes, B., Lina, A., A. Majumdar, Orban, D., C. Prior, & Zalzal, V. (2011). On equidistant points on a curve [Activity Report]. GERAD.

Orban, D. (2011). Templating and automatic code generation for performance with Python ({Cahier Du GERAD} G-2011-30). GERAD.

2010

Journal Articles

Fourer, R., Maheshwari, C., Neumaier, A., Orban, D., & Schichl, H. (2010). Convexity and concavity detection in computational graphs. INFORMS Journal on Computing, 22, 26–43. https://doi.org/10.1287/ijoc.1090.0321

Fourer, R., & Orban, D. (2010). The DrAMPL meta solver for optimization problem analysis. Computational Management Science, 7(4), 437–463. https://doi.org/10.1007/s10287-009-0101-z

Orban, D., V. Raymond, & Soumis, F. (2010). A new version of the improved primal simplex for degenerate linear programs. Computers and Operations Research, 37(1), 91–98. https://doi.org/10.1016/j.cor.2009.03.020

Proceedings

Audet, C., C.-K. Dang, & Orban, D. (2010). Algorithmic parameter optimization of the DFO method with the OPAL framework. In K. Naono, K. Teranishi, J. Cavazos, & R. Suda (Eds.), Software automatic tuning: From concepts to state-of-the-art results (first, pp. 255–274). Springer. https://doi.org/10.1007/978-1-4419-6935-4

J.-P. Harvey, Chartrand, P., Eriksson, G., & Orban, D. (2010). Gibbs energy minimization challenges using implicit variables solution models. TOFA: Discussion Meeting on Thermodynamics of Alloys.

2009

Journal Articles

Armand, P., A. Kiselev, Marcotte, O., & Orban, D. (2009). Self calibration of a pinhole camera. Mathematics-in-Industry Case Studies, 1, 81–98.

Unpublished

Orban, D. (2009). The lightning AMPL tutorial. A guide for nonlinear optimization users ({Cahier Du GERAD} G-2009-66). GERAD.

2008

Journal Articles

Armand, P., Benoist, J., & Orban, D. (2008). Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming. Computational Optimization and Applications, 41(1), 1–25. https://doi.org/10.1007/s10589-007-9095-z

Unpublished

Gould, N. I. M., Orban, D., & L. Toint, Ph. (2008). LANCELOT_SIMPLE: A simple interface for LANCELOT-b ({Cahier Du GERAD} G-2008-11). GERAD.

Orban, D. (2008). Projected Krylov methods for unsymmetric augmented systems ({Cahier Du GERAD} G-2008-46). GERAD.

2006

Journal Articles

Audet, C., & Orban, D. (2006). Finding optimal algorithmic parameters using the mesh adaptive direct search algorithm. SIAM Journal on Optimization, 17(3), 642–664. https://doi.org/10.1137/040620886

Waltz, R. A., Morales, J. L., Nocedal, J., & Orban, D. (2006). An interior algorithm for nonlinear optimization that combines line search and trust region steps. Mathematical Programming, 107(3), 391–408. https://doi.org/10.1007/s10107-004-0560-5

2005

Journal Articles

Gould, N. I. M., Orban, D., Sartenaer, A., & Toint, P. L. (2005). Sensitivity of trust-region algorithms to their parameters. 4OR, 3(3), 227–241. https://doi.org/10.1007/s10288-005-0065-y

Gould, N., Orban, D., & Toint, P. (2005). Numerical methods for large-scale nonlinear optimization. Acta Numerica, 14, 299–361. https://doi.org/10.1017/S0962492904000248

Proceedings

Menvielle, N., Goussard, Y., Orban, D., & Soulez, G. (2005). Reduction of beam-hardening artifacts in X-ray CT. Engineering in Medicine and Biology Society, 2005. 27th Annual International Conference of the IEEE-EMBS 2005., 1865–1868. https://doi.org/10.1109/IEMBS.2005.1616814

2003

Journal Articles

Gould, N. I. M., Orban, D., & Toint, Ph. L. (2003). CUTEr and SifDec: A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw., 29(4), 373–394. https://doi.org/10.1145/962437.962439

Gould, N. I. M., Orban, D., & Toint, Ph. L. (2003). GALAHAD, a library of thread-safe fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw., 29(4), 353–372. https://doi.org/10.1145/962437.962438

2002

Journal Articles

Gould, N. I. M., Orban, D., Sartenaer, A., & Toint, P. L. (2002). Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Mathematical Programming, 92(3), 481–508. https://doi.org/10.1007/s101070100287

Wright, S. J., & Orban, D. (2002). Properties of the log-barrier function on degenerate nonlinear programs. Mathematics of Operations Research, 27(3), 585–613. https://doi.org/10.1287/moor.27.3.585.312

Unpublished

Gould, N. I. M., Orban, D., & L. Toint, Ph. (2002). Results from a numerical evaluation of LANCELOT b (Internal Report NAGIR-2002-1). Rutherford Appleton Laboratory.

2001

Journal Articles

Gould, N. I. M., Orban, D., Sartenaer, A., & L. Toint, Philippe. (2001). Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM Journal on Optimization, 11(4), 974–1002. https://doi.org/10.1137/S1052623400370515

2000

Journal Articles

Conn, A. R., Gould, N. I. M., Orban, D., & Toint, P. L. (2000). A primal-dual trust-region algorithm for non-convex nonlinear programming. Mathematical Programming, 87(2), 215–249. https://doi.org/10.1007/s101070050112