Assistant Professor · Mathematics & Statistics · American University of Sharjah
Gabriel Jarry-Bolduc
I mainly study derivative-free optimization — how to minimize functions when gradients are unavailable — through the geometry of positive spanning sets, cosine measures, and gradient approximation techniques.
About
I am an assistant professor in the Department of Mathematics & Statistics at the American University of Sharjah. My research sits at the intersection of continuous optimization, nonsmooth analysis, and numerical analysis, with a particular focus on derivative-free optimization (DFO): algorithms that make progress using only function evaluations.
Much of my work concerns the geometry underlying these methods — how the structure of a positive spanning set, quantified by its cosine measure, governs the worst-case quality of a search direction, and how simplex gradients and Hessians can be built, combined, and analyzed through exact calculus rules and error bounds. Recent projects extend these ideas to nonsmooth finite-max functions and the convergence theory of iterative methods.
I also maintain an active interest in mathematics education research and am committed to supporting women in mathematics — a cause that was deeply important to my dear friend Dr. Mohabat Tarkeshian.
PhD in Mathematics, University of British Columbia (2023) · MSc, UBC (2019) · BSc, Université du Québec à Trois-Rivières (2017). My research is supported by an AUS Faculty Research Grant (2026) and an AUS Faculty Start-Up Grant (2026).
- derivative-free optimization
- positive spanning sets
- cosine measure
- simplex gradients & Hessians
- nonsmooth analysis
- numerical analysis
- convergence theory
- artificial intelligence
- mathematics education
Publications
Authors are listed alphabetically. Unless stated otherwise, all authors contributed equally.
IN PREPARATION
Positive bases of size 2n − 1 with maximal cosine measure
with M. Krishan Lal — in preparation · interactive figures (rotatable and adjustable versions of the paper's figures, and an explorer for the structure theorem).
SUBMITTED
A p-step generalization of the Q-order convergence
submitted to Mathematics · arXiv:2608.15202.
The cosine measure of a function at a point
with W. Hare & C. Planiden — submitted to Mathematics of Operations Research · arXiv:2608.07716.
An algorithm to exactly compute minimal upper bounds in the Loewner order
with A. Humeniuk, P. Pascua & N. Williams — submitted to Linear Algebra and Its Applications · arXiv:2606.18173.
2025
Using generalized simplex methods to approximate derivatives
with C. Planiden — IMA Journal of Numerical Analysis.
The cosine measure relative to a subspace
with C. Audet & W. Hare — Computational Optimization and Applications.
2024
with W. Hare, S. Kerleau & C. W. Royer — Linear Algebra and Its Applications 680, 183–207.
2023
A matrix algebra approach to approximate Hessians
with W. Hare & C. Planiden — IMA Journal of Numerical Analysis, 1–31.
Nicely structured positive bases with maximal cosine measure
with W. Hare & C. Planiden — Optimization Letters, 1–21.
with W. Hare — Algorithms 16(2), 84.
2022
Error analysis of surrogate models constructed through operations on sub-models
with Y. Chen & W. Hare — Mathematics of Operations Research.
with W. Hare & C. Planiden — Journal of Set-Valued and Variational Analysis.
Approximating the diagonal of a Hessian: which sample set of points should be used
Numerical Algorithms 91, 1349–1361.
2021
with P. Braun & W. Hare — Journal of Computational and Applied Mathematics 386, 113218.
2020
A deterministic algorithm to compute the cosine measure of a finite positive spanning set
with W. Hare — Optimization Letters 14, 1305–1316.
Error bounds for overdetermined and underdetermined generalized centred simplex gradients
with W. Hare & C. Planiden — IMA Journal of Numerical Analysis 42, 744–770.
Calculus identities for generalized simplex gradients: rules and applications
with W. Hare — SIAM Journal on Optimization 30(1), 853–884.
Uniform simplex of an arbitrary orientation
with P. Nadeau & S. Singh — Optimization Letters 14(6), 1407–1417.
Teaching
Recent courses at the American University of Sharjah:
- MTH 104Calculus II
- MTH 343Numerical Analysis
- MTH 565Numerical Analysis (graduate)
I am currently developing an optimization course at AUS, expected to be available in the Fall 2027 semester.
I have previously taught at UBC Okanagan, St. Francis Xavier University, Mount Royal University, and the University of Calgary. I had the privilege to teach courses spanning the calculus sequence, linear algebra, business mathematics, data modeling, and pre-calculus. Alongside my classroom work, I pursue research in mathematics education, including a study of student understanding of indeterminate forms.
Research group
I am open to new collaborations and to welcoming new students into my group, whether to conduct research on a project or for thesis supervision. Feel free to get in touch.
CURRENT — AMERICAN UNIVERSITY OF SHARJAH
- Dana AbukhalafMaster's student, 2026–
- Ranem ElashalUndergraduate student, 2026–
- Mariam Fadl El MulaUndergraduate student, 2026–
- Wissam HakawatiDoctoral student, 2026–
- Joud HamdanMaster's student, 2026–
- Syed Musab KazimUndergraduate student, 2026–
- Dr. Manish Krishan LalResearcher, 2026–
- Yassine LeducMaster's student, 2026–
- Mohamad TurkmaniMaster's student, 2026–
Supported by my AUS Faculty Research Grant and Faculty Start-Up Grant.
PAST — MOUNT ROYAL UNIVERSITY
- Joban BrarUndergraduate student, 2025
- Yanishka GahlotUndergraduate student, 2025
- Gaurav NeupaneUndergraduate student, 2025
- Patrick PascuaUndergraduate student, 2025 · co-supervised with Dr. Adam Humeniuk
- Nejaunie WilliamsUndergraduate student, 2025 · co-supervised with Dr. Adam Humeniuk
Supported by my NSERC Discovery Grant, MRU Internal Research Grant Funding, and an MRU Faculty of Science and Technology Student Research Award (Yanishka Gahlot).
Book an appointment
Students: you can book a meeting with me directly — pick any available slot below and it will be added to both our calendars automatically, with a confirmation sent to your email.
CV & contact
The best way to reach me is by email. I welcome inquiries from prospective graduate students interested in optimization, nonsmooth analysis, or numerical analysis.
Department of Mathematics & Statistics · American University of Sharjah · Sharjah, United Arab Emirates · +971 6 515 4423