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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
Arreckx, S. & Orban, D. (2018). A regularized factorization-free method for equality-constrained optimization. SIAM Journal on Optimization, 28(2), 1613-1639. Retrieved from https://doi.org/10.1137/16M1088570
Conference paper
Sinqueira, A.S. & Orban, D. (2018). A regularized interior-point method for constrained nonlinear least squares. Paper presented at the 12th Brazilian Workshop on Continuous Optimization, Foz do Iguaçu, Brazil.
Conference paper
Siqueira, A.S. & Orban, D. (2018). Developing new optimization methods with packages from the JuliaSmoothOptimizers organisation. Paper presented at the 2nd annual JuMP-Dev Workshop, Bordeaux, France (30 pages).
Conference paper
Ma, D., Judd, K.L., Orban, D. & Saunders, M.A. (2018). Stabilized optimization via an NCL algorithm. Paper presented at the 4th International Conference on Numerical Analysis and Optimization (NAO-IV 2017), Muscat, Oman (pp. 173-191). Retrieved from https://doi.org/10.1007/978-3-319-90026-1_8

Teaching

Optimisation, Mathématiques, Recherche opérationnelle.

Supervision at Polytechnique

IN PROGRESS

  • Master (thesis) (1)

    • Dahito, Marie-Ange. MINRES pour résoudre les sous-problèmes de région de confiance.

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 (9)

    • 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).