SPOT

Prochains exposés

SPOT 106 – Lundi 4 mai 2026 – Salle des thèses (C002) à l’ENSEEIHT (N7), 2 rue Charles Camichel, 31000 Toulouse

SPOT 105 – Mardi 14 avril 2026 15h30 - Exceptionnellement dans l’amphithéâtre Costes de l’ENAC, 7 avenue Edouard Belin, 31400 Toulouse

Sébastien Bourguignon (École Centrale Nantes) – Exact sparse optimization and beyond with branch-and-bound algorithms

Sparse coding in signal processing (also known as variable or subset selection in statistics) aims to approximate a data vector by a linear combination of a small number of elementary features drawn from a high-dimensional dictionary. While the original formulation leads to NP-hard optimization problems based on the $\ell_0$ “norm” (which counts the number of nonzero elements in a vector), most works in the field rely on relaxation techniques or heuristic methods. These approaches can handle very high-dimensional problems, but typically provide sparse solutions without guarantees, and rarely recover the global optimum.
In this talk, we will present different contributions developed in our research group, based on branch-and-bound algorithms that aim to solve exactly the $\ell_0$-norm formulation. Problems involving both standard sparsity and structured sparsity (where groups of variables are jointly constrained to be zero) are considered. Designing tailored continuous relaxations and associated algorithms is shown to play a key role in improving algorithmic efficiency. We show that the proposed algorithms may achieve better data fits than standard approaches on rather small, but difficult, sparse estimation problems, with a much higher, although « reasonable », computation time. A last part will be dedicated to the sparse spectral unmixing problem in signal processing, where sparse estimation is pushed beyond optimization: the branch-and-bound setting is then used to return, with guarantees, the exhaustive set of solutions satisfying acceptable misfit error and sparsity constraints.

Comité local d’organisation

Une séance par mois environ, avec deux conférenciers chaque fois (deux conférences de type différent : une orientée fondements et une orientée applications, un conférencier de l’environnement toulousain et un conférencier extérieur, un conférencier du milieu académique et un conférencier du milieu de l’industrie et des services, etc.).

Horaire habituel : le lundi après-midi de 14h à 16h.

Lieu

Sauf indication contraire, à la salle des thèses (C002) à l’ENSEEIHT (N7), 2 rue Charles Camichel, 31000 Toulouse  (métro B, François Verdier). Attention, présentez-vous au poste de garde afin d’accéder au site.