Laurent Granvilliers

Learn More
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)
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)
Traditional design of numerical software with result verification is based on the assumption that we know the algorithm that transforms input into the output , 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)