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 51 articles , 2 standard articles )

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  1. Martin, Benjamin; Correia, Marco; Cruz, Jorge: A certified branch & bound approach for reliability-based optimization problems (2017)
  2. Martin, Benjamin; Goldsztejn, Alexandre; Granvilliers, Laurent; Jermann, Christophe: Constraint propagation using dominance in interval branch & bound for nonlinear biobjective optimization (2017)
  3. Tung, Vu Xuan; Khanh, To Van; Ogawa, Mizuhito: raSAT: an SMT solver for polynomial constraints (2017)
  4. Bagnara, Roberto; Carlier, Matthieu; Gori, Roberta; Gotlieb, Arnaud: Exploiting binary floating-point representations for constraint propagation (2016)
  5. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  6. Martin, Benjamin; Goldsztejn, Alexandre; Granvilliers, Laurent; Jermann, Christophe: On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach (2016)
  7. Tung, Vu Xuan; Khanh, To Van; Ogawa, Mizuhito: raSAT: an SMT solver for polynomial constraints (2016)
  8. Goldsztejn, Alexandre; Jermann, Christophe; Ruiz de Angulo, Vicente; Torras, Carme: Variable symmetry breaking in numerical constraint problems (2015)
  9. Kubica, Bartłomiej Jacek: Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems (2015)
  10. Narkawicz, Anthony; Muñoz, César; Dutle, Aaron: Formally-verified decision procedures for univariate polynomial computation based on Sturm’s and Tarski’s theorems (2015)
  11. Ninin, Jordan; Messine, Frédéric; Hansen, Pierre: A reliable affine relaxation method for global optimization (2015)
  12. Wechsung, Achim; Scott, Joseph K.; Watson, Harry A. J.; Barton, Paul I.: Reverse propagation of McCormick relaxations (2015)
  13. Caro, S.; Chablat, D.; Goldsztejn, A.; Ishii, D.; Jermann, C.: A branch and prune algorithm for the computation of generalized aspects of parallel robots (2014)
  14. Duracz, Jan; Konečný, Michal: Polynomial function intervals for floating-point software verification (2014)
  15. Goualard, Frédéric: How do you compute the midpoint of an interval? (2014)
  16. Thabet, Rihab El Houda; Raïssi, Tarek; Combastel, Christophe; Efimov, Denis; Zolghadri, Ali: An effective method to interval observer design for time-varying systems (2014)
  17. Carvalho, Elsa; Cruz, Jorge; Barahona, Pedro: Probabilistic constraints for nonlinear inverse problems (2013)
  18. Gao, Sicun; Kong, Soonho; Clarke, Edmund M.: dReal: an SMT solver for nonlinear theories over the reals (2013)
  19. Muñoz, César; Narkawicz, Anthony: Formalization of Bernstein polynomials and applications to global optimization (2013)
  20. Patil, Mukesh D.; Nataraj, P. S. V.: QFT prefilter design for multivariable systems using interval constraint satisfaction technique (2013)

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