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Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper first presents HC4, an algorithm to enforce hull consistency without decomposing complex constraints into… (More)

RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or… (More)

Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦ ¨ § © £ © that transforms input , and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm ¦ , we only know some relation (constraints)… (More)

In this paper we present a framework for the cooperation of symbolic and propagation-based numerical solvers over the real numbers. This cooperation is expressed in terms of xed points of closure operators over a complete lattice of constraint systems. In a second part we instantiate this framework to a particular cooperation scheme, where propagation is… (More)

Parameter estimation is the problem of finding the values of the unknowns of a mathematical model for simulating a complex system. A model is generally given by differential equations or systems of equations or inequalities. Interval computations are numerical computations over sets of real numbers. In this paper intervals are used to model uncertainty in… (More)

Constraint programming can definitely be seen as a model-driven paradigm. The users write programs for modeling problems. These programs are mapped to executable models to calculate the solutions. This paper focuses on efficient model management (definition and transformation). From this point of view, we propose to revisit the design of… (More)

This paper presents the first implementation of COMMA, a new solver independent language for modeling constraint-based problems. The combination of a constraint language with an object-oriented framework represents the base of the core of COMMA. Extension capabilities have also been included with the aim of tackling a wide range of applications from… (More)

A new branch-and-prune algorithm for globally solving nonlinear systems is proposed. The pruning technique combines a multidimensional interval Newton method with the constraint satisfaction algorithm HC4 [1]. The main contributions of this paper are the fine-grained interaction between both algorithms which avoids some unnecessary computation, and the… (More)