Hi, I’m Pierre Vernimmen.
I work on the worst-case analysis and design of first-order optimization methods. In practice, this means that I spend a fair amount of time asking simple-looking questions such as “how bad can gradient descent really be?” and then trying to answer them exactly.
My main tools are Performance Estimation Problems, Lyapunov analysis, semidefinite programming, and computer-assisted proofs. I mostly work on smooth (strongly) convex optimization, exact and inexact gradient methods, and accelerated schemes. I am also interested in stochastic optimization, and their practical implementations.
About
I am a PhD student in applied mathematics at UCLouvain, in the Institute of Information and Communication Technologies, Electronics and Applied Mathematics. My research sits at the intersection of mathematical optimization, numerical analysis, and semidefinite programming.
I like methods that are simple to state but surprisingly subtle to understand. Gradient descent is a perfect example: one line of code, many possible convergence measures, and a lot of interesting mathematics hiding behind the constants.
Research
A large part of my work is based on the Performance Estimation Problem methodology. The idea is to formulate the worst-case behavior of an optimization algorithm as another optimization problem. The numerical solution gives a sharp guarantee, and the dual certificate often contains the proof we were looking for.
I am particularly interested in tight convergence guarantees, gradient-norm bounds, robust step-size schedules, relatively inexact gradients, and the way numerical certificates can be transformed into clean analytical arguments.
People
I am supervised by François Glineur . I also work with Adrien Taylor and Baptiste Goujaud on topics related to Performance Estimation, first-order methods, and worst-case analysis.
Publications and manuscripts
A sharp worst-case analysis of gradient descent with relatively inexact gradients on smooth convex functions, using the Performance Estimation Problem framework.
A numerical and computer-assisted study of the robustness of long-step and accelerated methods under relatively inexact gradients.
A conference paper on relatively inexact gradient descent for smooth convex optimization.
My master’s thesis, focused on tight convergence guarantees for exact and inexact gradient methods with constant and silver step-size schedules.
I usually link to the DOI, arXiv, proceedings, or institutional repository rather than hosting separate local copies of papers here. It keeps the page cleaner, and it avoids versioning and copyright headaches.
Teaching
I am involved in teaching and exercise sessions in optimization and applied mathematics at UCLouvain. I particularly enjoy helping students turn a mathematical model into something that can actually be solved, plotted, interpreted, and debugged without too much suffering.
- Optimization courses and exercise sessions at bachelor and master level.
- Student projects involving mathematical modeling, linear programming, and numerical optimization.
Contact
Affiliation
UCLouvain
Institute of Information and Communication Technologies,
Electronics and Applied Mathematics
Louvain-la-Neuve, Belgium
Links
Email:
pierre.vernimmen@uclouvain.be
Google Scholar:
Pierre Vernimmen
ORCID:
0009-0004-9578-6823
GitHub:
Verpierre