Société de Mathématiques Appliquées et Industrielles

Le prix de thèse PGMO

Le Programme Gaspard Monge pour l’optimisation et la recherche opérationnelle, avec la participation et le patronage scientifique de la ROADEF et de la SMAI (groupe MODE), patronne chaque année deux prix de thèse (1000€ chacun).

Lauréats 2018

- Nicolas Flammarion. Many problems in machine learning are naturally cast as the minimization of a smooth function defined on a Euclidean space. While small problems are efficiently solved by classical optimization algorithms, large-scale problems are typically solved with first-order techniques based on gradient descent. Nicolas Flammarion considers, in his thesis, the particular case of the quadratic loss. He addresses its minimization when gradients are only accessible through a stochastic oracle and proposes optimal algorithms in different cases. His work offers many perspectives of applications of the quadratic loss in machine learning. Clustering and estimation with shape constraints are the two first applications already considered.

- Nicolas Bonifas. The work of Nicolas Bonifas falls in the scope of constraint-based scheduling. In this framework, the most frequently encountered resource constraint is the cumulative, which enables the modeling of parallel processes. In his thesis, Nicolas studies the cumulative constraint with the help of tools rarely used in constraint programming (polyhedral analysis, linear programming duality, projective geometry duality) and propose two contributions for the domain. Cumulative strengthening is a means of generating tighter redundant cumulative constraints, analogous to the generation of cuts in integer linear programming. This is one of the first examples of a redundant global constraint. Energy Reasoning is an extremely powerful propagation for cumulative constraint, with hitherto a high complexity of O(n^3). Nicolas proposes an algorithm that computes this propagation with a O(n^2 log n) complexity, which is a significant improvement of this algorithm known for more than 25 years.

Le jury pour l’édition 2018 était présidé par Mathilde Mougeot et composé de :

- Membres désignés par la ROADEF

Céline Gicquel, Université Paris-Sud
Sandra Ulrich Ngueveu, LAAS, CNRS
Michael Poss, Université de Montpellier

- Membres désignés par le groupe SMAI-MODE

Jean Baptiste Caillau, Université de la Côte d’Azur
Thierry Champion, Université de Toulon.
Aude Rondepierre, INSA de Toulouse

- Membres désignés par le Conseil Scientifique du PGMO

Mathilde Mougeot, ENSIIE et Université Paris-Diderot, Présidente du Jury
Gabriel Peyré, ENS, CNRS
Nicolas Vieille, HEC

Lauréats 2017

- Vincent Cohen-Addad. This thesis contains pathbreaking and practically very important results concerning local search heuristics for clustering (k-means, k-median) and network design (traveling salesman, Steiner tree). It establishes some structural properties under which these local search heuristics perform very well and even yield polynomial time approximation schemes for these problems.

- Joon Kwon. The thesis begins with a remarkably clear presentation of the basics of online linear optimization, regret minimization, mirror descent and approachability. The author develops the analysis of the classical problem of prediction with expert advice in which the outcome vector is assumed to be sparse, and design of optimal approachability strategies for the problem of prediction under partial monitoring. The author also shows how a continuous mirror descent motivates a large set of minimization algorithms in discrete time and the thesis ends with an elegant result bounding variations of convex functions.

Le jury pour l’édition 2017 était présidé par Guillaume Carlier et composé de :

- Membres désignés par la ROADEF

Clarisse Dhaenens, CRIStAL, Université de Lille
Marcel Mongeau, ENAC
Sourour Elloumi, ENSTA

- Membres désignés par le groupe SMAI-MODE

Guillaume Carlier, CEREMADE (Président)
Anatoli Juditsky, Laboratoire Jean Kuntzmann, Grenoble
Jalal Fadili, ENSICAEN

- Membres désignés par le Conseil Scientifique du PGMO

Luce Brotcorne, INRIA Lille
Julien Mairal, INRIA Grenoble
Jérôme Renault, Toulouse School of Economics

Lauréats 2016

- Pauline Sarrabezolles. Pauline Sarrabezolles obtained her PhD thesis in Applied Mathematics at Université Paris-Est and ENPC ParisTech under the supervision of Frédéric Meunier. The title of the thesis is "colorful linear programming" and it stands at the intersection of discrete mathematics, combinatorics, optimization, graph theory and algorithmics. Colorful linear programming is an extension of linear programming where the variables are assigned to different categories (colors) and their number in each category is bounded. It has many applications in geometry and complex optimization problems. She studied the complexity of some algorithms like a colorful version of the simplex algorithm and proved a combinatorial conjecture in connection with the colorful Carathéodory theorem. The jury was impressed by the unique combination of various skills used by Pauline Sarrabezolles to solve these problems.

- Bruno Ziliotto. Bruno Ziliotto obtained his PhD thesis in Applied Mathematics at Université de Toulouse under the supervision of Jérôme Renault. Its title is "Stratégies et paiements de long terme dans les jeux répétés à deux joueurs" and it is concerned with asymptotics of repeated zero-sum games, possibly with stochastic aspects. In particular it disproves a long-standing conjecture on the existence of a limit value and of a limit optimal strategy for the player. By the dynamic programming approach, this result has a link with the homogenization of stochastic Hamilton-Jacobi equations. More precisely, Bruno Ziliotto also found a striking counter-example of a non-convex Hamiltonian for which no stochastic homogenization occurs. The jury particularly appreciated the various and deep results obtained in different areas of mathematics and optimization.

La remise des prix aura lieu lors des journees PGMO les 8 et 9 novembre 2016. Plus d’informations ici.

Ci-après la liste des membres du jury 2016 :

- Membres désignés par la ROADEF

Eric Gourdin, Orange Labs
Christelle Jussien, Université d’Angers
Aziz Moukrim, UTC

- Membres désignés par le groupe SMAI-MODE

Francis Bach, INRIA Paris et ENS
Maitine Bergounioux, Université d’Orléans
Michel de Lara, ENPC

- Membres désignés par le Conseil Scientifique du PGMO

Mariann Akian, INRIA Saclay—Ile-de-France et CMAP
Grégoire Allaire, CMAP, École polytechnique
Marie-Christine Costa, UMA, ENSTA et CEDRIC

Lauréats 2015

- Benjamin Martin. Benjamin Martin prepared his PhD thesis in Nantes in Computer Science after a Bachelor in Mathematics at the University of Nantes and a Master Degree in Computer Science at the University of Nantes too. The thesis directed and co-directed by Laurent Granvilliers, Alexandre Goldsztejn, Christophe Jermann is titled « Rigorous Algorithms for non-linear biobjective optimization ». The thesis deals with the interval based rigorous algorithm, i.e. with guaranteed results, to solve biobjective problems. The candidate proposes a certified continuation method that tracks locally a connected manifold of optimal solutions, which supplements other techniques from the literature. The proposed method adapts finely to the shape of manifolds and deals with singularities resulting from inequality constraints in biobjective problems. Moreover, the candidate develops an interval Branch & Bound (B&B) algorithm that globally computes a verified enclosure of the optimal solutions. This method integrates constraint propagation techniques, noticeably exploiting bounds on the objectives, in order to enhance the solving process. The jury particularly appreciated the fact that the thesis presents both strong theoretical and applied results.

Samuel Vaiter. Samuel Vaiter did is PhD thesis in Mathematics at the Univerity Paris Dauphine under the direction of Gabriel Peyré. He studied Computer Science and Mathematics at the ENS Lyon (Bachelor) and ENS Cachan (Master) respectively. The thesis is titled « Low Complexity Regularization of Inverse Problems ». This thesis is concerned with recovery guarantees and sensitivity analysis of variational regularization for noisy linear inverse problems. This is cast as a convex optimization problem by combining a data fidelity and a regularizing functional promoting solutions conforming to some notion of low complexity related to their non-smoothness points. This thesis makes a very nice contribution to the field of linear inverse problems, convex geometry and analysis. The candidate has provided a unified framework for analyzing the robustness (vis a vis noise) and sensitivity of solutions to the inverse problem. The results are sharp enough to recover some of the known results for special instances. At the same time, the framework is general enough to accommodate most regularizers used in practice. The jury particularly appreciated the fact that Samuel Vaiter was able to put under a single umbrella a series of techniques and results for treating a variety of problems.

Lauréats 2014

- Daniel HOEHENER. Daniel HOEHENER prepared his PhD thesis at Université Pierre et Marie Curie (Paris 6) on "Conditions d’optimalité pour des problèmes de contrôle optimal avec contraintes d’états’’ (Optimality conditions for some optimal control problems with state constaints), supervised by Hélène Frankowska. His thesis includes several original results about second order conditions, proven under more general assumptions than the results already existing in literature, expressed in primal form, and involving both state and control constraints. The jury committee was impressed by the novelty of the results in a very technical domain, which also gave rise to excellent publications.

- Miquel OLIU BARTON. Miquel OLIU BARTON prepared his PhD thesis in Paris 6, under the supervision of Sylvain Sorin. The dissertation, on "Jeux dynamiques à information incomplète en temps discret et continu" (Dynamical games with incomplete information in dicrete and continuous time) is mainly devoted to the long-time behavior in differential and repeated games and control problems, and to games with lack of information. The jury committee appreciated the impressive amount of works and the novelty of the results, and in particular the new proof that M. Oliu Barton gave of the existence of a limit for the value in discounted games, with new and self contained techniques.

Lauréats 2013

- Olivier Fercoq a fait sa thèse sous la direction de Stéphane Gaubert et Marianne Akian (Inria-Saclay et CMAP, Ecole Polytechnique). Le sujet était : "Optimisation de vecteurs propres de Perron et applications : du référencement de pages web à la chonothérapie." Cette thèse constitue une "contribution majeure dans le domaine de l’optimisation de fonctions d’utilité sur l’ensemble des matrices positives" (selon l’un des rapporteurs). Elle présente à la fois un ensemble de résultats théoriques (propriétés, analyse de complexité, ...) et des applications intéressantes.

- Thibaut Vidal a fait sa thèse sous la direction de Michel Gendreau, Theodor Crainic et Christian Prins, avec une co-tutelle entre les universités de Montréal et Troyes (GERAD+LOSI). Le sujet était : "General solution approaches for multi-attribute vehicle routing and scheduling problems". Cette thèse peut être vue comme "un recueil des résultats les plus intéressants et les plus marquants des dernières décades dans le domaine des recherche de solutions heuristiques pour les tournées de véhicules" (selon l’un des rapporteurs) et "un pas en avant dans la quête d’une approche générale de résolution d’une large palette de problèmes de tournées" (selon l’autre). Elle présente des résultats génériques concernant les méta-heuristiques pour les problèmes riches de tournées et pouvant être étendus à d’autres problèmes, une analyse complète de ces problèmes et s’appuie sur de lourdes réalisations informatiques.

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