Mohamed Laghdaf Habiboullah

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About

I design and analyze optimization algorithms, the methods computers use to find the best possible solution to a problem, and I turn them into open-source software.

Portrait of Mohamed Laghdaf Habiboullah

PhD candidate in applied mathematics

I am a PhD candidate at Polytechnique Montréal and a student member of GERAD, supervised by Professors Youssef Diouane and Dominique Orban.

My research is on numerical optimization. I study trust-region and quasi-Newton methods for problems that are nonsmooth and nonconvex, as in sparse signal recovery, low-rank matrix completion or machine learning. I prove worst-case guarantees on how much work these methods need, and I implement them in Julia as a contributor to the JuliaSmoothOptimizers organization.

Before moving to Montréal, I studied applied mathematics at ENSTA Paris and Institut Polytechnique de Paris, and completed the MVA master (Mathematics, Vision, Learning).

  • Position: PhD candidate, 2023–2027
  • Lab: GERAD, Dept. of Mathematics and Industrial Engineering
  • City: Montréal, Canada
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Research & projects

Each project has its own page, written for a broad audience: what the problem is, what we did and why it matters, with the technical details at the end for specialists.

PhD research

arXiv preprint · 2026New

Complexity analysis of trust-region methods under (α, L0, L1)-smoothness

Many modern objectives, in particular in deep learning, are much steeper in places than classical theory allows. We study how trust-region methods cope with them.

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SIAM J. Optimization · 2026

R2N: A proximal modified quasi-Newton method for nonsmooth regularized optimization

A new algorithm, with guarantees and a Julia implementation, for problems that combine data fitting with a nonsmooth penalty such as sparsity or low rank.

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Software · JOSS · 2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

An open-source Julia package that puts trust-region and regularization methods for nonsmooth problems in everyone's hands.

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Mathematical Programming · 2026

Complexity of trust-region methods in the presence of unbounded Hessian approximations

How much work does a classical method need when the curvature information it relies on grows without bound? We give sharp answers, and address a question raised by Powell in 2010.

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Publications

Preprints

  1. Complexity analysis of trust-region methods under (α, L0, L1)-smoothness
    Youssef Diouane, Mohamed Laghdaf Habiboullah, Awa Khouna, Dominique Orban
    arXiv:2609.33238, 2026
    Project page arXiv

Journal articles

  1. A proximal modified quasi-Newton method for nonsmooth regularized optimization
    Youssef Diouane, Mohamed Laghdaf Habiboullah, Dominique Orban
    SIAM Journal on Optimization, 36(2):534–563, 2026
    Project page DOI arXiv
  2. RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization
    Maxence Gollier, Mohamed Laghdaf Habiboullah, Geoffroy Leconte, Robert Baraldi, Alberto De Marchi, Dominique Orban, Youssef Diouane
    Journal of Open Source Software, 11(118):9344, 2026
    Project page DOI Code
  3. Complexity of trust-region methods in the presence of unbounded Hessian approximations
    Youssef Diouane, Mohamed Laghdaf Habiboullah, Dominique Orban
    Mathematical Programming, 2026
    Project page DOI arXiv

Resume

Education

PhD in Applied Mathematics

2023 – 2027 (expected)

Polytechnique Montréal & GERAD, Montréal, Canada

  • Supervisors: Professors Youssef Diouane and Dominique Orban.
  • GPA 4.0; all courses validated with A*/A+.
  • Courses: operations research, continuous optimization, derivative-free optimization, optimal control, numerical linear algebra.

Master M2 MVA – Mathematics, Vision, Learning

2022 – 2023

Télécom Paris / Institut Polytechnique de Paris, France

  • One of the most selective master's programs in AI and machine learning in France. Honors: very good (mention très bien).
  • Courses: research project, deep learning, object recognition and computer vision, computational statistics, operations research, reinforcement learning, foundations of distributed and large-scale optimization.

Master M1 in Applied Mathematics

2021 – 2022

Institut Polytechnique de Paris, France

  • Ranked 49th in the world and 2nd in France (QS World University Rankings 2022).
  • Courses: probability (Markov chains and martingales), statistics, operations research, linear and nonlinear optimization, partial differential equations.

Engineering degree, Applied Mathematics

2020 – 2023

ENSTA Paris, France

  • Cumulative GPA 4.05. Data science and optimization track.
  • Applied mathematics, computer science, human and social sciences, and entrepreneurship.

Research experience

Research internship: second-order methods for large-scale optimization

April 2023 – September 2023

GERAD, Montréal, Canada

  • Developed new methods for large-scale nonsmooth optimization.
  • Started the paper later published in the SIAM Journal on Optimization (project page).
  • Wrote tests and automation scripts.
  • Supervisors: Professors Youssef Diouane and Dominique Orban.

Research internship: optimization of the matrix completion problem

May 2022 – August 2022

GERAD, Montréal, Canada

  • Modeled matrix completion as a rank-minimization problem.
  • Modeled and implemented the proximal operator of the rank function and contributed to Julia libraries.
  • Weakened the assumptions on the model of the nonsmooth term.
  • Supervisor: Professor Dominique Orban. Runner-up for the best research project prize at ENSTA Paris.

Internship: network administration

July 2021 – August 2021

SNIM (Société Nationale Industrielle et Minière de Mauritanie), Nouadhibou, Mauritania

  • Network segmentation of the company network, designed with Cisco Packet Tracer.
  • Supervisor: Khatary Mohamed Abdellahi Khattari, network administrator, IT department.

Skills

Programming

  • Julia
  • Python
  • C/C++
  • SQL
  • R
  • MATLAB

Machine learning

  • PyTorch
  • TensorFlow

Tools

  • Git
  • VS Code
  • Jupyter
  • Anaconda

Languages

  • Arabic (native)
  • French (bilingual)
  • English (C1, Linguaskill Cambridge)

Awards & scholarships

  • 2025FRQNT Doctoral Scholarship, Fonds de recherche du Québec – Nature et technologies ($83,334)Selected among the top 22% of doctoral candidates across all disciplines in Québec.
  • 2025Vanier Canada Graduate Scholarship – finalistOne of the top 4 candidates across all engineering disciplines at Polytechnique Montréal.
  • 2022 – 2023GERAD Research ScholarshipInternship funding for two consecutive years ($3,500 + $1,750).
  • 2022 – 2023ENSTA Paris Excellence Scholarship ($7,518)
  • 2022IVADO Undergraduate Research Scholarship ($7,000)
  • 2022Best research project prize, ENSTA Paris – runner-upMatrix completion project at GERAD; among the top 10 research projects, grade A*.
  • 2021Top 10% of the class, first year of the engineering program at ENSTA Paris (205 students, GPA 3.99)
  • 2020 – 2023Mauritanian Government Excellence Scholarship
  • 2018Ranked 2nd nationally, Mauritanian high-school diploma (baccalauréat)
  • 2018Ranked 5th, National Physics Olympiad, Mauritania
  • 2017Ranked 2nd, National Rally of Sciences, Mauritania

Teaching & service

Teaching

  • 2025 – 2026Teaching assistant, MTH2302B and MTH2312: Probability and StatisticsPolytechnique Montréal, Sep. 2025 – Apr. 2026.
  • Fall 2024Teaching assistant, MTH6412B: Implementation of Operations Research AlgorithmsPolytechnique Montréal, Sep. – Dec. 2024.
  • 2024 – 2026Math tutor, CCMPolytechnique Montréal. Helping undergraduate students with their mathematics questions and homework.

Service & open source

Talks

  • July 2025International Conference on Continuous Optimization (ICCOPT 2025), Los Angeles, USASession chair and speaker: “Complexity of trust-region methods in the presence of unbounded Hessian approximations”.
  • July 2024International Symposium on Mathematical Programming (ISMP 2024), Montréal, Canada“A proximal modified quasi-Newton method for nonsmooth regularized optimization”.
  • 2024 – 2025 – 2026Optimization Days (JOPT), HEC Montréal, CanadaThree talks on my PhD projects.

Contact

Feel free to reach out about research, collaborations or open-source work.

Email

mohamed-laghdaf-2.habiboullah@polymtl.ca

GitHub

molhab

Office

GERAD & Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Montréal, Canada