Mardi 10 Mars

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Mardi 10 Mars
Heure: 12:30 - 13:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Multiband Robust Optimization: theory and applications
Description: Fabio D'Andreagiovanni Over the last years, Robust Optimization (RO) has emerged as an effective and efficient
methodology to tackle data uncertainty in real-world optimization problems. RO takes into
account data uncertainty in the shape of hard constraints that restrict the feasible set and
maintain only robust solutions, i.e. solutions that remain feasible even when the values of the
input data change.
In this talk, we provide an overview of our research about theory and applications of RO.
Specifically, we present Multiband Robustness, a new model for RO that we recently
proposed to generalize and refine the classical Gamma-robustness model by Bertsimas and
Sim. The main aim of our new model is to provide a refined representation of arbitrary non-
symmetric distributions of the uncertainty, that are commonly present in real-world
applications. Such refined representation grants a reduction in conservatism of robust
solutions, while maintaining the accessibility and computational tractability that have been a
key factor of success of Gamma-robustness. We also provide an overview of applications of
the Multiband model to real-world problems that we have considered in past and ongoing
research and industrial projects.
Heure: 14:00 - 17:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Une généralisation des mots de Christoffel en dimension d.
Description: Sébastien Labbé In this work, we extend the definition of Christoffel words todirected subgraphs of the hypercubic lattice in arbitrary dimensionthat wecall Christoffel graphs. Christoffel graphs when $d=2$ correspond towell-known Christoffel words.We show that Christoffel graphs have similar properties to those ofChristoffel words: symmetry of their central part and conjugation withtheirreversal. Our main result extends Pirillo's theorem (characterization ofChristoffel words which asserts that a word $amb$ is a Christoffelword if andonly if it is conjugate to $bma$) in arbitrary dimension.In the generalization, the map $ambmapsto bma$ is seen as a flipoperation ongraphs embedded in $mathbb{Z}^d$ and the conjugation is a translation.We show that a fully periodic subgraph of the hypercubic lattice is atranslate of its flip if and only if it is a Christoffel graph.This is joint work with Christophe Reutenauer.Preprint is available at