# Project : coprin

## Section: Overall Objectives

Keywords : constraints programming, interval analysis, symbolic-numerical calculation, numerical robustness, systems solving, optimal design, software engineering, robotics, mechanism theory, quantum mechanics.

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 and optimization algorithms based on constraints propagation methods, interval analysis and symbolic computation, with interval arithmetic as the primary tool.

We are interested in real-valued constraint satisfaction problems
((f(X) = 0, f(X)0)), in optimization problems and in the proof
of the existence of properties (for example it exists
X such that f(X) = 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 arithmetic 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 and as the usual worst case analysis leads
to exponential complexity for problems that are not representative of
the application cases we are considering, the efficiency of the
algorithm will be
experimentally evaluated
through `IcosAlias` on various realistic bench examples.

Dissemination is also an essential component of our activity as interval analysis based methods are not sufficiently known in the engineering and academic communities.