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Dominique Orban
B. Maths, Ph.D. (FUNDP Namur, INP Toulouse)

Research interests and affiliations

Research interests

I am a computational mathematician. My research interests revolve around the design of specialized numerical algorithms for continuous nonlinear optimization and systems of nonlinear equations. Equally important is the practical application of those methods. This involves a mixture of numerical linear algebra, numerical analysis and programming. I am particularly interested in degeneracy and ill-posed problems. Typical fields of application include image reconstruction, optimal structure design, PDE-constrained optimization, and more.

Keywords: continuous nonlinear optimization, numerical linear algebra, numerical analysis.

Expertise type(s) (NSERC subjects)
  • 2705 Software and development
  • 2713 Algorithms
  • 2715 Optimization
  • 2955 Numerical analysis
  • 2956 Optimization and optimal control theory

Publications

Recent publications
Journal article
Migot, T., Orban, D. & Siqueira, A.S. (2022). DCISolver.jl : a julia solver for onlinear optimization using dynamic control of infeasibility. Journal of Open Source Software, 7(70), 4 pages. Retrieved from https://doi.org/10.21105/joss.03991
Conference paper
Ma, D., Orban, D. & Saunders, M.A. (2021). A Julia Implementation of Algorithm NCL for Constrained Optimization. Paper presented at the 5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer (NAOV 2020), Muscat, Oman (pp. 153-182). Retrieved from https://doi.org/10.1007/978-3-030-72040-7_8
Journal article
Ma, D., Orban, D. & Saunders, M.A. (2021). A Julia implementation of Algorithm NCL for constrained optimization. Cahiers du Gerad, 2021(02), 19 pages. Retrieved from https://www.gerad.ca/en/papers/G-2021-02
Journal article
di Serafino, D. & Orban, D. (2021). Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems. SIAM Journal on Scientific Computing, 43(2), 1001-1026. Retrieved from https://doi.org/10.1137/19M1291753

Teaching

Optimisation, Mathématiques, Recherche opérationnelle.

Supervision at Polytechnique

COMPLETED

  • Ph.D. Thesis (4)

    • Arreckx, S. (2016). Méthodes sans factorisation pour l'optimisation non linéaire (Ph.D. Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/2213/
    • Towhidi, M. (2013). Treatment of Degeneracy in Linear and Quadratic Programming (Ph.D. Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/1112
    • Coulibaly, Z. (2012). Traitement de la dégénérescence en optimisation non linéaire (Ph.D. Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/956
    • Dang, C.K. (2012). Optimization of algorithms with the OPAL framework (Ph.D. Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/870
  • Master's Thesis (11)

    • Lotfi, S. (2020). Stochastic First and Second Order Optimization Methods for Machine Learning (Master's Thesis, Polytechnique Montréal). Retrieved from https://publications.polymtl.ca/5457/
    • Mestagh, G. (2019). Méthodes mises à l'échelle pour la reconstruction tomographique en coordonnées cylindriques (Master's Thesis, Polytechnique Montréal). Retrieved from https://publications.polymtl.ca/4050/
    • Dahito, M.-A. (2018). La méthode des résidus conjugués pour calculer les directions en optimisation continue (Master's Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/3281/
    • Demeester, K. (2017). Méthodes numériques appliquées à la programmation dynamique stochastique pour la gestion d'un système hydroélectrique (Master's Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/2695/
    • McLaughlin, M. (2017). Méthodes sans factorisation pour la tomographie à rayons-X en coordonnées cylindriques (Master's Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/2742/
    • Lakhmiri, D. (2016). Un environnement pour l'optimisation sans dérivées (Master's Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/2266/
    • Dehghani, M. (2013). A Regularized Interior-Point Method for Constrained Linear Least Squares (Master's Thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/1121
    • Curatolo, P.-R. (2008). Méthodes de pénalisation pour l'optimisation de structures (Master's Thesis, École Polytechnique de Montréal).
    • Fidahoussen, C.A. (2008). Méthodes itératives pour la résolution par éléments finis d'écoulements à surfaces libres (Master's Thesis, École Polytechnique de Montréal).
    • Omer, J. (2006). Méthode de réduction dynamique de contraintes pour un programme linéaire (Master's Thesis, École Polytechnique de Montréal).
    • Menvielle, N. (2004). Réduction des artéfacts métalliques en tomographie à rayons X (Master's Thesis, École Polytechnique de Montréal).