Algorithm 852 Realpaver: nonlinear constraint solving & rigorous global optimization. Problems: Realpaver allows modeling and solving nonlinear and nonconvex constraint satisfaction and optimization problems over the real numbers. The decision variables, continuous or discrete, have to be bounded. Functions and constraints have to be defined by analytical expressions involving usual arithmetic operations and transcendental elementary functions. Rigourousness: Realpaver covers the solution set of a given problem by means of rectangular regions from the real Euclidean space. It can prove the problem insatisfiability by calculating an empty covering. Under some conditions, it can prove the existence of solutions to a set of constraints. Moreover, it is able to enclose the global optimum of an optimization problem with certainty. Solving methods: Realpaver implements correctly rounded interval-based computations in a branch-and-bound framework. Its key feature is to combine several methods from various fields: interval fixed-point operators, constraint propagation and local consistency techniques, local optimization using descent methods and metaheuristics, and several search strategies. Package: Realpaver is open source, configurable, object-oriented, and ISO C++ compliant. The API allows the extension of the library along with modeling and solving problems. A mathematical modeling language and a set of benchmarks are also provided. Interval arithmetic is supported by gaol. (Source:

References in zbMATH (referenced in 50 articles , 2 standard articles )

Showing results 41 to 50 of 50.
Sorted by year (citations)
  1. Yamamura, Kiyotaka; Suda, Koki; Tamura, Naoya: LP narrowing: A new strategy for finding all solutions of nonlinear equations (2009)
  2. Jansson, Christian; Chaykin, Denis; Keil, Christian: Rigorous error bounds for the optimal value in semidefinite programming (2008)
  3. Apt, Krzysztof R.; Zoeteweij, Peter: An analysis of arithmetic constraints on integer intervals (2007)
  4. Beaumet, Grégory; Verfaillie, Gérard; Charmeau, Marie-Claire: Estimation of the minimal duration of an attitude change for an autonomous agile earth-observing satellite (2007)
  5. Granvilliers, Laurent; Benhamou, Frédéric: Algorithm 852: RealPaver: An interval solver using constraint satisfaction techniques. (2006)
  6. Neveu, Bertrand; Chabert, Gilles; Trombettoni, Gilles: When interval analysis helps inter-block backtracking (2006)
  7. Xia, Songtao; Di Vito, Ben; Munoz, Cesar: Predicate abstraction of programs with non-linear computation (2006)
  8. Lebbah, Yahia; Michel, Claude; Rueher, Michel: A rigorous global filtering algorithm for quadratic constraints (2005)
  9. Monfroy, Eric; Saubion, Frédéric; Lambert, Tony: On hybridization of local search and constraint propagation (2004)
  10. Granvilliers, Laurent; Monfroy, Eric: Implementing constraint propagation by composition of reductions. (2003)

Further publications can be found at: