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 & research
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 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).
- derivative-free optimization
- positive spanning sets
- cosine measures
- simplex gradients & Hessians
- nonsmooth analysis
- numerical analysis
- convergence theory
- mathematics education
Publications
Authors are listed alphabetically, following the convention in mathematics; all authors contributed equally.
SUBMITTED
Cosine measure of a function at a point
with W. Hare & C. Planiden — submitted to Mathematics of Operations Research.
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 have previously taught at UBC Okanagan, St. Francis Xavier University, Mount Royal University, and the University of Calgary — 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.
I currently supervise a research group at AUS — a researcher and doctoral, master's, and undergraduate students — supported by my Faculty Research Grant.
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