Première rencontre nationale du RT Optimisation

Liste des Contributions

15. Mots d'accueil

26/11/2025 14:00

10. APPROXIMATION OF BLASCHKE-SANTAL'O DIAGRAMS

Edouard Oudet (Université Grenoble Alpes)

26/11/2025 14:05

Identifying Blaschke-Santal´o diagrams is an important topic that
essentially consists in determining the image Y = F (X) of a map F : X →
Rd, where the dimension of the source space X is much larger than the
one of the target space. In some cases, that occur for instance in shape
optimization problems, X can even be a subset of an infinite-dimensional
space. The usual Monte Carlo method,...

17. A phase field approximation for the Reifenberg Plateau's problem : existence and regularity of solutions

Eve Machefert (Institut Camille Jordan)

26/11/2025 14:50

The goal of this work is to use a phase field method to approximate the notorious Plateau problem, which consists of finding a surface of minimum area that spans a given curve. To this aim, we want to generalise to Plateau’s problem, using a Reifenberg formulation, the functional introduced by M. Bonnivard, A. Lemenant, and F. Santambrogio for Steiner’s problem (searching for the shortest path...

16. Branched Optimal Transport and Fractal Measures in Type-I Superconductors

Alessandro Cosenza (Université Paris Cité)

26/11/2025 15:35

In this talk I will introduce a branched transport problem with weakly imposed boundary conditions. This problem was first derived as a reduced model for pattern formation in type-I superconductors in [1]. For minima of the reduced model with weak boundary conditions, it is conjectured in [2] that the dimension of the boundary measure is non-integer. The conjecture was linked to local scaling...

9. Deterministic Mean Field Games with jumps

Annette Dumas (Université de Limoges)

26/11/2025 16:45

The Mean Field Game we consider is motivated by the modelization of the housing dynamics where each inhabitant can move from one place to another. In particular, the trajectories of the agents are piecewise constant and they minimize a cost consisting in the number of jumps (or relocations) and two terms depending on the density: the first one is variational and the other one is...

7. A tentative phase-field approach for the curvature flow of non-oriented boundaries

Antonin Chambolle (CEREMADE, CNRS & Université Paris-Dauphine)

26/11/2025 17:30

In this talk, we start from a neural-net based approach developed by
Bretin et al (Bretin, Denis, Masnou, Terii, 2022), which extends the
classical phase-field method for the mean curvature flow of boundaries
to the case of non-oriented interfaces. We introduce an analytical,
energy-based approach which yields an evolution PDE reproducing the
numerical experiments obtained with the neural...

11. Dynamic Splitting Games

Jérôme Renault (TSE (Université Toulouse 1 Capitole))

27/11/2025 09:40

We consider zero-sum dynamic games of information revelation. Each player controls a martingale of beliefs by choosing in each period a particular splitting (balayée) of the current belief, and the payoffs are determined by the limit beliefs. We introduce constraints on the set of available splittings, and characterize the value of the game as the unique solution of an extended...

3. Coordination mechanisms with Partially Specified Probabilties

M. Francesco Giordano (HEC)

27/11/2025 10:25

Decision makers act based on the data they observe. However, the nature of the true data-generating process is often only partially known: we model such partial knowledge as a set of moment conditions. Given the partial information available, we consider an heuristic model of belief formation derived from the maximization of the Shannon entropy. This paper characterizes the outcomes that can...

6. Session Posters (et pause café)

27/11/2025 11:10

Jules Berry : Mean Field Games on networks with sticky transition conditions.

Adrien Cances : Discrétisation lagrangienne pour la résolution numérique d'un problème de transport multi-marginal

Giuseppe Carrino : Numerical frugality in optimization: mixed-precision Newton's method

Benjamin Capdeville : Discrete-to-continuum convergence of gradient flow structures for the Moran process...

14. Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback

Vianney Perchet (ENSAE & Criteo AI Lab)

27/11/2025 12:30

In this talk, I will introduce the problem of learning in zero-sum game, and especially for the problem of "last-iterate" convergence, unlike the traditional literature that looks at the average convergence (we argue it makes more sense). The interesting property is that the optimal rate is T^{-1/4} which is quite unusual (and unexpected) in this literature.

18. Optimal control of systems described by measures: motivation, challenge and perspectives

Charles Bertucci (Université Paris-Dauphine & CNRS)

27/11/2025 14:50

I will motivate the study of optimal control problems of systems described by positive measures, namely for optimization and large deviations of mean field systems. I will explain why the associated Hamilton-Jacobi equation plays a crucial role in these problems, as well as the main mathematical challenges it raises. I will focus in particular on the difficulties arising when trying to prove a...

19. Propagation d'une notion de log-concavité faible le long des flots de chaleur généralisés

Katharina Eichinger (Université Paris-Saclay & INRIA)

27/11/2025 15:35

Une conséquence bien connue de l’inégalité de Prékopa–Leindler est la préservation de la log-concavité par le semi-groupe de la chaleur. Cette propriété ne s’étend cependant pas aux semi-groupes plus généraux. Nous étudions donc une notion de log-concavité plus faible qui peut être propagée le long de semi-groupes de chaleur généralisés.
Nous en déduisons des plusieurs propriétés. Ici, je...

5. The competitive spectral radius of families of nonexpansive mappings

Marianne AKIAN (Inria and CMAP)

27/11/2025 16:45

We introduce a new class of perfect information repeated zero-sum games in which the payoff of one player is the escape rate of a switched dynamical system which evolves according to a nonexpansive nonlinear operator depending on the actions of both players. This is motivated by applications to population dynamics (growth maximization and minimization).

Considering order preserving finite...

20. A gradient flow for every c(x,y) cost: EVI-inspired convexity

Pierre-Cyril Aubin (ENPC)

27/11/2025 17:30

How to go beyond the square distance d^2 in optimization algorithms and flows in metric spaces? Replacing it with a general cost function c(x,y) and using a majorize-minimize framework I will detail a generic class of algorithms encompassing Newton/mirror/natural/Riemannian gradient descent/Sinkhorn/EM by reframing them as an alternating minimization, each for a different cost c(x,y). Rooted...

4. New advances in the complexity analysis of SGD

Guillaume Garrigos (LPSM)

28/11/2025 09:40

This talk will showcase new results about the Stochastic Gradient Descent (SGD) algorithm for solving convex and smooth stochastic problems. After introducing the algorithm and its main features (convergence rates vs complexity, notion of interpolation) we will present two new results.

In the first part, we ask ourselves: what are the best possible complexity bounds one can hope for SGD?...

13. Restarted Truncated unrolled networks to bridge the gap between Plug-and-Play and Unfolded Neural Networks for image restoration

Nelly PUSTELNIK

28/11/2025 10:25

In recent years, deep learning methods have transformed the field of image restoration, achieving significantly higher reconstruction quality than traditional variational approaches. Many current strategies combine principles from both variational models and neural networks, forming what are known as model-based neural networks. Among these, two main frameworks stand out: Unfolded neural...

8. Principes de comparaison pour des problèmes variationels et application aux transports optimaux.

Maxime Sylvestre (Université Paris Dauphine PSL CEREMADE)

28/11/2025 11:45

Nous étudions des problèmes variationnels dans des espaces de Banach faisant intervenir des énergies sous-modulaires. Nous étendons la notion de substituabilité à ce cadre de dimension infinie et montrons qu’elle est en dualité avec la sous-modularité. Ces deux notions nous permettent de dériver des principes de comparaison de manière abstraite. Nous appliquons ensuite nos résultats aux...

21. The Entropic JKO Scheme

Aymeric Baradat

28/11/2025 12:30

The JKO scheme (named after Jordan, Kinderlehrer, and Otto, 1996) is an implicit Euler-type scheme that provides a variational way to construct weak solutions to nonlinear diffusion equations, relying on their gradient flow structure in the Wasserstein space. In 2015, Peyré proposed an entropic version which, although it only yields approximate solutions to the original problem, leads to...

12. Sur une inégalité isopérimétrique quantitative dans le plan

Gisella Croce (Université Paris 1)

28/11/2025 14:50

Ce séminaire portera sur des avancées récentes sur une inégalité isopérimétrique quantitative dans le plan, avec une contrainte géométrique.
Plus précisément si $\Omega$ est un ouvert borné, nous étudierons l'inégalité de type
$$ \delta(\Omega)\geq C \lambda_0^2(\Omega,B)\,, $$ où $\delta(\Omega)$ est le déficit isopérimétrique (différence entre le périmètre de $\Omega$ et le...

2. Training dynamics of ReLU Networks: a Path-lifting Perspective

Rémi GRIBONVAL (Inria)

28/11/2025 15:35

Can we hope to decipher the role of the well-known rescaling symmetries of ReLU networks parameterizations in their training dynamics ? The talk will explore recent advances in this direction that exploit the path-lifting, a rescaling-invariant polynomial representation of the parameters of general ReLU networks. Despite its combinatorial dimension, the path-lifting turns out to be not only a...