Project : coprin

Section: Overall Objectives

Keywords : constraints programming , interval analysis , symbolic-numerical calculation , numerical robustness , systems solving , robotics , mechanism theory , molecular chemistry .

Overall Objectives

COPRIN is a joint project between Nice/Sophia-Antipolis University (UNSA), CNRS, ENPC and INRIA. Its scientific objective is to develop and implement systems solving algorithms based on constraints propagation methods, interval analysis and symbolic computation, with interval arithmetics as the primary tool.

We are interested in real-valued constraint satisfaction problems (( $f\left(X\right)=0$ , $f\left(X\right)\le 0$ )), in optimization problems and in the proof of the existence of properties (for example it exists X such that $f\left(X\right)=0$ or it exists two values $X_1$ , $X_2$ such that $f(X_1)>0$ and $f(X_2)<0$ )

Solutions will be searched within a finite domain (called a box) which may be either continuous or mixed (i.e. for which some variables must belong to a continuous range while other variables may only have value within a discrete set). An important point is that we aim to find all the solutions within the domain as soon as the computer arithmetics will allow it: in other words we are looking for certified solutions.

Our research aims to develop algorithms that can be used for any problem or are specific to a given class of problem, especially problems that are issued from application domains for which we have an internal expertise (such as mechanism theory and software engineering).

Implementation of the algorithms will be performed within the frameworks of the generic software tool IcosAlias, currently under development, whose purpose is to allow one to design and test solving algorithms obtained as the combination of various software modules. IcosAlias will be based on the already existing libraries ICOS and ALIAS.

As a theoretical complexity analysis of the solving algorithms is usually extremely difficult, the efficiency of the algorithms will be experimentally evaluated through IcosAlias on various bench examples.