# OptAzur: Optimization in French Riviera #

OptAzur is an ongoing effort to foster collaborations among members of Université Côte d’Azur on different aspect of optimization and its applications to machine learning, imaging and signal processing, etc.

## Seminar #

OptAzur organizes a monthly seminar in Nice and Sophia-Antipolis, which alternates between the two sites and takes place on the third Monday of each month.

Indico Calendar (and subscription)

### Next talk #

Monday, June 3rd, 2024 (I3S, Sophia-Antipolis)

14h - Emmanuel Soubies (CNRS, IRIT, ENSEEIHT)

**Exact Continuous Relaxations of L0-Regularized Generalized Linear Models**

Sparse generalized linear models are widely used in fields such as statistics, computer vision, signal/image processing and machine learning. The natural sparsity promoting regularizer is the l0 pseudo-norm which is discontinuous and non-convex. In this talk, we will present the l0-Bregman relaxation (B-Rex), a general framework to compute exact continuous relaxations of such l0-regularized criteria. Although in general still non-convex, these continuous relaxations are qualified as exact in the sense that they let unchanged the set of global minimizer while enjoying a better optimization landscape. In particular, we will show that some local minimizers of the initial functional are eliminated by these relaxations. Finally, these properties will be illustrated on both sparse Kullback-Leibler regression and sparse logistic regression problems.

15h15 - Luc Pronzato (CNRS, I3S)

**Safe screening rules in convex optimisation: some examples in optimal design of experiments**

Many convex optimisation problems can be formulated as the minimisation of a convex function of a probability measure over a given set. Typical examples include determining the ellipsoid of minimum volume, or the smallest ball, containing a set of points. When it is known in advance that the optimal measure will be supported by a small number of points, it is advantageous to eliminate unnecessary points (candidates) in order to simplify the problem. Safe screening rules aim to eliminate such points: a rule defines a test to be applied to the candidates in order to eliminate those that are useless; a rule is safe when no point supporting an optimal measure is eliminated. The aim is to apply the screening rule during optimisation, regardless of the optimisation algorithm used. Usually, the efficiency of elimination increases when approaching the optimum, so the rule should be applied several (many) times and be as simple as possible. In addition to the construction of ellipsoids and balls of minimal volume, I will present the construction of screening rules for different criteria in optimal design of experiments, some of them with a link to (quadratic) Lasso. Parts of this work are based on collaborations with Radoslav Harman (Comenius University, Bratislava) and Guillaume Sagnol (TU Berlin).

### Previous talks #

Titles and abstracts here

- #1: Jean-François Aujol (Université de Bordeaux) and Luca Calatroni (CNRS, I3S)
- #2: Gersende Fort (CNRS, Institut de Mathématiques de Toulouse) and Samuel Vaiter (CNRS, Laboratoire J. A. Dieudonné)
- #3: Massimiliano Pontil (Italian Institute of Technology and University College London) and Mathieu Carrière (Inria)
- #4: Maurizio Filippone (EURECOM) and Yassine Laguel (Laboratoire J. A. Dieudonné)
- #5: Marco Lorenzi (Inria)
- #6: Juan Peypouquet (University of Groningen) and Khazhgali Kozhasov (LJAD, Nice)
- #7: Aris Daniilidis (VADOR, TU Wien) and Wellington de Oliveira (Mines Paris)
- #8: Lorenzo Rosasco (University of Genova and MIT) and Lénaïc Chizat (EPFL)

## Events #

The members organize several conferences and workshops relevant to the optimization community, as detailled below.

Bilevel optimization in machine learning and imaging sciences workshop @ICIAM 2023, Tokyo, Japan. (Organizers: L. Calatroni, S. Vaiter)

Optimal control: methods and applications @ICIAM 2023, Tokyo, Japan. (Organizers: J.-B. Caillau, L. Dell’Elce, Clément Moreau)

## Scientific Committee #

- Laure Blanc-Féraud
- Luca Calatroni (co-organizer)
- Jean-Baptiste Caillau
- Yassine Laguel
- Samuel Vaiter (co-organizer)