Gilles Chabert

Gilles CHABERT

Ph.D. in Computer Science
HEPHAISTOS project of INRIA

Reseach interests
Publications
Software
Teaching
Personal
Address

Research interests

I am working on algorithmic & numerical methods for robust system solving. My fields of study include:

Interval analysis, systems of equations with quantified parameters. Here is a very short 2-pages introduction to interval analysis.
Solver design
Constraint propagation, local consistencies with unions of intervals

Publications

G. Chabert, and A. Goldsztejn
Extension of the Hansen-Bliek Method to Right-Quantified Linear Systems
Reliable Computing (to appear)

C. Grandón, G. Chabert, and B. Neveu
Generalized Interval Projection: A New Technique for Consistent Domain Extension
IJCAI - Twientieth International Joint Conference on Artificial Intelligence , Hyderabad, India, 2007

A. Goldsztejn, and G. Chabert
On the Approximation of Linear AE-Solution Sets
SCAN - 12th International Symposion on Scientific Computing, Computer Arithmetic and Validated Numerics , Duisburg, Germany, 2006

B. Neveu, G. Chabert, and G. Trombettoni
When Interval Analysis Helps Inter-Block Backtracking
CP - 12th International Conference on Principles and Practice of Constraint Programming , Nantes, France, 2006

D. Daney, N. Andreff, G. Chabert, and Y. Papegay
Interval Method for Calibration of Parallel Robots: A Vision-based Experimentation
Mechanism and Machine Theory, Elsevier, 2006

A. Goldsztejn, and G. Chabert
A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems
NMA - 6th International Conference on Numerical Methods and Applications, Borovets, Bulgaria, 2006

G. Trombettoni, and G. Chabert
Constructive Interval Disjunction
IntCP - Interval analysis, constraint propagation, application, Nantes, France, 2006

G. Chabert, G. Trombettoni and B. Neveu
Box-Set Consistency for Interval-Based Constraint Problems
SAC - 20th ACM Symposium on Applied Computing, Santa Fe, USA, 2005

G. Chabert, G. Trombettoni and B. Neveu
IGC: Une Nouvelle Consistance Partielle pour les CSPs Continus
JFPC - Journées Francophones de Programmation par Contraintes, Lens, France, 2005

G. Chabert, G. Trombettoni and B. Neveu
New Light on Arc Consistency over Continuous Domains
Rapport de recherche INRIA RR-5365, 2004

G. Chabert, G. Trombettoni and B. Neveu
New Light on Arc-Consistency over Continuous Domains
1st International Workshop on Constraint Propagation and Implementation, Toronto, Canada, 2004

G. Chabert
Techniques d'intervalles pour la résolution de systèmes d'équations
Ph.D. Thesis, University of Nice-Sophia Antipolis, 2007

(manuscript 1.6Mo)

(slides 2.5Mo)

Software

Throughout my PHD, I have spent some effort to implement and maintain a C++ interval-based library for constraint solving (over the reals).

Several members of the HEPHAISTOS project have been using this library since 2004 for various purposes (calibration of parallel robots, geometric constraints), and it is intended to become a more open project.

Some performance comparisons between my library and other famous ones (Real Paver, Ilog Solver, Alias) shall be available soon on this page. It is still under development & validation so there is no source code to download yet.

Basic features

Interval arithmetic layer : A wrapper of Bias/Profil routines (mainly to handle bugs and manage infinite bounds)
Evaluations : Natural (Kahan) extension, automatic differentiation, mean value form, extensions in Kaucher arithmetic.
Interval linear package : preconditionning, Gauss elimination, Gauss Seidel, Krawczyk, Hansen-Bliek, generalized Gauss-Seidel & Shary's auxiliary equation.
Contractors : Automatic projection, Hull consistency (Benhamou), 3B (Lhomme), Box (Benhamou, Van Hentenryck) and other shaving techniques.
Newton-based methods: Univariate Newton (Hansen), Hansen-Sengupta, non-linear Krawczyk.
bisection heuristics: Round-robin, blockwise, largest domain, deepest descent.

High-level features

An AMPL-compatible modeling langage.
A general-purpose fully customizable solver.
Inner tests & filtering procedures under parameters uncertainty, combining parameter splitting and a generalized Hansen-Sengupta operator (Goldsztejn).
Subsystem generation and filtering for chains of systems obtained via decomposition methods (Neveu, Trombettoni & Jermann)

Teaching

2005-2006 (Polytech'Nice engineering school)