Aravkin, A., R. Baraldi, & Orban, D. (2021). A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization (Cahier Du GERAD No. G-2021-12). doi: 10.13140/RG.2.2.18509.15845/1
Ma, D., Saunders, M. A., & Orban, D. (2021). A Julia Implementation of Algorithm NCL for Constrained Optimization (Cahier Du GERAD No. G-2021-02). doi: 10.13140/RG.2.2.29888.35841
2020
Journal Articles
Mestdagh, G., Goussard, Y., & Orban, D. (2020). Scaled Projected-Direction Methods with Application to Transmission Tomography. Optimization and Engineering, 1–25. doi: 10.1007/s11081-020-09484-0
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. doi: 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. doi: 10.1137/19M1255069
Orban, D., & Siqueira, A. S. (2020). A Regularization Method for Constrained Nonlinear Least Squares. Computational Optimization and Applications, 76, 961–989. doi: 10.1007/s10589-020-00201-2
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. doi: 10.1137/19M1290991
Conference Articles
Lotfi, S., Bonniot de Ruisselet, T., Orban, D., & Lodi, A. (2020). Stochastic Damped L-BFGS with Controlled Norm of the Hessian Approximation. doi: 10.13140/RG.2.2.27851.41765/1
Technical Reports
A Ghannad, Orban, D., & Saunders, M. A. (2020). A Symmetric Formulation of the Linear System Arising in Interior Methods for Convex Optimization with Bounded Condition Number (Cahier Du GERAD No. G-2020-37). doi: 10.13140/RG.2.2.17742.28483
A. Montoison, & Orban, D. (2020). TriCG and TriMR: Two Iterative Methods for Symmetric Quasi-Definite Systems (Cahier Du GERAD No. G-2020-41). doi: 10.13140/RG.2.2.12344.16645
2019
Journal Articles
M. Dehghani, A. Lambe, & Orban, D. (2019). A Regularized Interior-Point Method for Constrained Linear Least Squares. INFOR: Information Systems and Operational Research. doi: 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. doi: 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. doi: 10.1137/16M1094816
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. doi: 10.1137/17M1113552
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. doi: 10.1137/18M1194948
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. doi: 10.1137/18M1194900
Technical Reports
di Serafino, D., & Orban, D. (2019). Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems (Cahier Du GERAD No. G-2019-72). doi: 10.5281/zenodo.3926751
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. doi: 10.1137/16M1088570
Orban, D. (2018). Introduction to Computation and Programming Using Python. Second Edition, with Application to Understanding Data. SIAM Review, 60(2), 483–485.
Conference Articles
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 (pp. 173–191). doi: 10.1007/978-3-319-90026-1_8
2017
Books
Orban, D., & Arioli, M. (2017). Iterative Solution of Symmetric Quasi-Definite Linear Systems. doi: 10.1137/1.9781611974737
Technical Reports
Côté, P., K. Demeester, Orban, D., & M. Towhidi. (2017). Numerical Methods for Stochastic Dynamic Programming with Application to Hydropower Optimization (Cahier Du GERAD No. G-2017-64). doi: 10.13140/RG.2.2.32660.81280
Goussard, Y., M. McLaughlin, & Orban, D. (2017). Factorization-Free Methods for Computed Tomography (Cahier Du GERAD No. G-2017-65). doi: 10.13140/RG.2.2.17141.88808
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 No. G-2017-70). doi: 10.13140/RG.2.2.25690.24008
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. doi: 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 No. G-2016-42). doi: 10.13140/RG.2.1.2846.6803
2015
Journal Articles
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. doi: 10.1007/s11081-015-9287-9
Orban, D., & M. Towhidi. (2016). Customizing the solution Process of COIN-OR’s Linear Solvers with Python. Mathematical Programming Computation, 8(4), 377–391. doi: 10.1007/s12532-015-0094-2
Gould, N. I. M., Orban, D., & Toint, P. L. (2015). CUTEst: a Constrained and Unconstrained Testing Environment
with safe threads for Mathematical Optimization. Computational Optimization and Applications, 60, 545–557. doi: 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. doi: 10.1007/s11075-014-9933-x
Conference Articles
Gould, N. I. M., Orban, D., & Toint, P. L. (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 (pp. 117–150). doi: 10.1007/978-3-319-17689-5
Technical Reports
Dussault, J.-P., & Orban, D. (2015). A Scalable Implementation of Adaptive Cubic Regularization Methods Using Shifted Linear Systems (Cahier Du GERAD No. G-2015-109). Montréal, QC, Canada: GERAD.
Orban, D. (2015). A Collection of Linear Systems Arising from Interior-Point Methods for Quadratic Optimization (Cahier Du GERAD No. G-2015-117). Montréal, QC, Canada: GERAD.
2014
Journal Articles
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. doi: 10.1137/120890600
Audet, C., C.-K. Dang, & Orban, D. (2014). Optimization of Algorithms with OPAL. Mathematical Programming Computation, 6(3), 233–254. doi: 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. doi: 10.1137/130916394
Technical Reports
Orban, D. (2014). The Projected Golub-Kahan Process for Constrained
Linear Least-Squares Problems (Cahier Du GERAD No. G-2014-15). Montréal, QC, Canada: 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. doi: 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. doi: 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. doi: 10.1080/10556788.2012.668905
Friedlander, M. P., & Orban, D. (2012). A Primal-Dual Regularized Interior-Point Method for Convex Quadratic Programs. Mathematical Programming Computation, 4(1), 71–107. doi: 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. doi: 10.1137/090777232
Armand, P., & Orban, D. (2012). The Squared Slacks Transformation in Nonlinear Programming. Sultan Qaboos University Journal for Science, 17(1), 22–29.
Technical Reports
Dehghani, A., Goffin, J.-L., & Orban, D. (2012). Solving Unconstrained Nonlinear Programs Using ACCPM (Cahier Du GERAD No. G-2012-02). Montréal, QC, Canada: GERAD.
Miscellaneous
Orban, D. (2013). Numerical Optimization in the Python Ecosystem. Montréal, QC, Canada: 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. doi: 10.1007/s11590-011-0428-6
Technical Reports
Orban, D. (2011). Templating and Automatic Code Generation for Performance with Python (Cahier Du GERAD No. G-2011-30). Montréal, QC, Canada: GERAD.
Ayotte-Sauvé, E., M. Chugunova, Cortes, B., Lina, A., A. Majumdar, Orban, D., … Zalzal, V. (2011). On Equidistant Points on a Curve [Activity Report]. Montréal, QC, Canada: GERAD.
2010
Journal Articles
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. doi: 10.1016/j.cor.2009.03.020
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. doi: 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. doi: 10.1007/s10287-009-0101-z
Book Chapters
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). doi: 10.1007/978-1-4419-6935-4
Conference Articles
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.
Technical Reports
Orban, D. (2009). The Lightning AMPL Tutorial. A Guide for Nonlinear Optimization Users (Cahier Du GERAD No. G-2009-66). Montréal, QC, Canada: 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. doi: 10.1007/s10589-007-9095-z
Technical Reports
Gould, N. I. M., Orban, D., & Toint, P. L. (2008). LANCELOT_SIMPLE: A Simple Interface for LANCELOT-B (Cahier Du GERAD No. G-2008-11). Montréal, QC, Canada: GERAD.
Orban, D. (2008). Projected Krylov Methods for Unsymmetric Augmented Systems (Cahier Du GERAD No. G-2008-46). Montréal, QC, Canada: 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. doi: 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. doi: 10.1007/s10107-004-0560-5
2005
Journal Articles
Gould, N., Orban, D., & Toint, P. (2005). Numerical methods for large-scale nonlinear optimization. Acta Numerica, 14, 299–361. doi: 10.1017/S0962492904000248
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. doi: 10.1007/s10288-005-0065-y
Conference Articles
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. doi: 10.1109/IEMBS.2005.1616814
2003
Journal Articles
Gould, N. I. M., Orban, D., & Toint, P. L. (2003). CUTEr and SifDec: A Constrained and Unconstrained Testing Environment, Revisited. ACM Trans. Math. Softw., 29(4), 373–394. doi: 10.1145/962437.962439
Gould, N. I. M., Orban, D., & Toint, P. L. (2003). GALAHAD, a Library of Thread-safe Fortran 90 Packages for Large-scale Nonlinear Optimization. ACM Trans. Math. Softw., 29(4), 353–372. doi: 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. doi: 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. doi: 10.1287/moor.27.3.585.312
Technical Reports
Gould, N. I. M., Orban, D., & Toint, P. L. (2002). Results from a Numerical Evaluation of LANCELOT B (Internal Report No. NAGIR-2002-1). Chilton, UK: Rutherford Appleton Laboratory.
2001
Journal Articles
Gould, N. I. M., Orban, D., Sartenaer, A., & Philippe L. Toint. (2001). Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming. SIAM Journal on Optimization, 11(4), 974–1002. doi: 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. doi: 10.1007/s101070050112