Project : coprin
Section: New Results
Keywords : constraint programming, interval analysis, symbolic-numerical calculation, numerical robustness, systems solving, constraint satisfaction problems (CSP), global optimization.
Systems solving in continuous domains
Systems solving and optimization are clearly the core of our research activities. We focus on systems solving as many applications in engineering sciences require finding all isolated solutions to systems of constraints over real numbers. It is difficult to solve as the inherent computational complexity is NP-hard and numerical issues are critical in practice. For example, it is far from being obvious to guarantee correctness and completeness as well as to ensure termination. Overall complexity of our solvers cannot be estimated in general and consequently only extensive experiments allow to estimate their practical complexity which is in general quite different from the worst case exponential complexity.
Our research focus on the following axis:
developing new algorithms for local and global filtering, exclusion and existence operators. This is one of the main axis of our theoretical work. It involves numerical analysis, symbolic computation, constraints programming.
developing specific solvers for systems sharing the same type of structure (e.g. systems of distance equations or linear interval systems as mentioned later on). Here also a theoretical work allows to specialize the mathematical tools we are using according to the problem at hand for a better efficiency. In parallel specific data structure are used in the implementation
systems decomposition: the objective is to decompose large systems into sub-systems that are independent or loosely connected and are solved in sequence, allowing an important improvement of efficiency compared to general solver 
developing our generic systems solving software IcosAlias. Existing solvers exhibit lack of flexibility: our objective is to develop a framework that will allow to modify easily the solving strategy, to test new algorithms and to develop solvers for specific systems
The theoretical work of this year addresses systems of geometrical constraints and distance equations (subjects on which we are working since the very beginning of the project), optimization (a theme that we have planned to consider for a long time as interval analysis is one of the very few methods that allows for global optimization) and linear systems (a topic that is important both for the applications and for the interval analysis algorithms)