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 )

Showing results 21 to 40 of 51.
Sorted by year (citations)
  1. Gao, Sicun; Avigad, Jeremy; Clarke, Edmund M.: (\delta)-complete decision procedures for satisfiability over the reals (2012)
  2. Ishii, Daisuke; Goldsztejn, Alexandre; Jermann, Christophe: Interval-based projection method for under-constrained numerical systems (2012)
  3. Misener, Ruth; Floudas, Christodoulos A.: Global optimization of mixed-integer models with quadratic and signomial functions: a review (2012)
  4. Passmore, Grant Olney; Paulson, Lawrence C.; de Moura, Leonardo: Real algebraic strategies for MetiTarski proofs (2012)
  5. Patil, Mukesh D.; Nataraj, P. S. V.; Vyawahare, Vishwesh A.: Automated design of fractional PI QFT controller using interval constraint satisfaction technique (ICST) (2012)
  6. Skjäl, A.; Westerlund, T.; Misener, R.; Floudas, C. A.: A generalization of the classical (\alpha)BB convex underestimation via diagonal and nondiagonal quadratic terms (2012)
  7. Yamamura, Kiyotaka; Tamura, Naoya: Finding all solutions of separable systems of piecewise-linear equations using integer programming (2012)
  8. Bartocci, Ezio; Grosu, Radu; Katsaros, Panagiotis; Ramakrishnan, C. R.; Smolka, Scott A.: Model repair for probabilistic systems (2011)
  9. Nataraj, P. S. V.; Arounassalame, M.: Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm (2011)
  10. Domes, Ferenc; Neumaier, Arnold: Constraint propagation on quadratic constraints (2010)
  11. Goldsztejn, Alexandre; Granvilliers, Laurent: A new framework for sharp and efficient resolution of NCSP with manifolds of solutions (2010)
  12. Nataraj, P. S. V.; Kalla, Rambabu: Computation of spectral sets for uncertain linear fractional-order systems (2010)
  13. Neveu, Bertrand; Trombettoni, Gilles; Chabert, Gilles: Improving inter-block backtracking with interval Newton (2010)
  14. Niveau, Alexandre; Fargier, Hélène; Pralet, Cédric; Verfaillie, Gérard: Knowledge compilation using interval automata and applications to planning (2010)
  15. Raïssi, Tarek; Videau, Gaétan; Zolghadri, Ali: Interval observer design for consistency checks of nonlinear continuous-time systems (2010)
  16. Revol, Nathalie: Standardized interval arithmetic and interval arithmetic used in libraries (2010)
  17. Chabert, Gilles; Jaulin, Luc: Contractor programming (2009)
  18. De Angulo, V. Ruiz; Torras, C.: Exploiting single-cycle symmetries in continuous constraint problems (2009)
  19. Maher, Michael J.: Local consistency for extended CSPs (2009)
  20. Vu, Xuan-Ha; Sam-Haroud, Djamila; Faltings, Boi: Enhancing numerical constraint propagation using multiple inclusion representations (2009)

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