RealPaver swMATH ID: 4401 Software Authors: Laurent Granvilliers Description: 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. Homepage: http://pagesperso.lina.univ-nantes.fr/~granvilliers-l/realpaver/ Programming Languages: C Related Software: Numerica; INTOPT_90; gaol; ICOS; dReal; RSOLVER; libMC; GLOPTLAB; BARON; MetiTarski; INTLAB; PROFIL/BIAS; CPLEX; Boost Interval Arithmetic; GloptiPoly; SeDuMi; SCIP; Gappa; PVS; Coq Cited in: 51 Publications Further Publications: http://pagesperso.lina.univ-nantes.fr/~granvilliers-l/realpaver/ Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Estimation of the minimal duration of an attitude change for an autonomous agile earth-observing satellite. Zbl 1145.68504Beaumet, Grégory; Verfaillie, Gérard; Charmeau, Marie-Claire 2007 Algorithm 852: RealPaver: An interval solver using constraint satisfaction techniques. Zbl 1346.65020Granvilliers, Laurent; Benhamou, Frédéric 2006 all top 5 Cited by 98 Authors 6 Goldsztejn, Alexandre 5 Granvilliers, Laurent 5 Jermann, Christophe 4 Nataraj, Paluri S. V. 3 Chabert, Gilles 3 Floudas, Christodoulos Achilleus 3 Misener, Ruth 3 Muñoz, César A. 2 Clarke, Edmund Melson jun. 2 Cruz, Jorge T. M. 2 Gao, Sicun 2 Ishii, Daisuke 2 Khanh, To Van 2 Martin, Benjamin T. 2 Monfroy, Eric 2 Narkawicz, Anthony Joseph 2 Neveu, Bertrand 2 Ogawa, Mizuhito 2 Patil, Mukesh D. 2 Raissi, Tarek 2 Sam-Haroud, Djamila 2 Tamura, Naoya 2 Torras, Carme 2 Trombettoni, Gilles 2 Tung, Vu Xuan 2 Verfaillie, Gérard 2 Vu, Xuan-Ha 2 Yamamura, Kiyotaka 2 Zolghadri, Ali 1 Apt, Krzysztof Rafal 1 Arounassalame, M. 1 Avigad, Jeremy 1 Bagnara, Roberto 1 Barahona, Pedro 1 Bartocci, Ezio 1 Barton, Paul I. 1 Beaumet, Grégory 1 Benhamou, Frédéric 1 Boukouvala, Fani 1 Carlier, Matthieu 1 Caro, Stéphane 1 Carvalho, Elsa 1 Chablat, Damien 1 Charmeau, Marie-Claire 1 Chaykin, Denis 1 Combastel, Christophe 1 Correia, Marco 1 De Angulo, V. Ruiz 1 de Moura, Leonardo 1 Di Vito, Ben L. 1 Domes, Ferenc 1 Duracz, Jan 1 Dutle, Aaron 1 Efimov, Denis V. 1 Faltings, Boi Volkert 1 Fargier, Hélène 1 Gori, Roberta 1 Gotlieb, Arnaud 1 Goualard, Frédéric 1 Grosu, Radu 1 Hansen, Pierre 1 Jansson, Christian 1 Jaulin, Luc 1 Kalla, Rambabu 1 Katsaros, Panagiotis 1 Keil, Christian 1 Konečný, Michal 1 Kong, Soonho 1 Kubica, Bartłomiej Jacek 1 Lambert, Tony 1 Lebbah, Yahia 1 Maher, Michael J. 1 Messine, Frédéric 1 Michel, Claude 1 Neumaier, Arnold 1 Ninin, Jordan 1 Niveau, Alexandre 1 Passmore, Grant Olney 1 Paulson, Lawrence Charles 1 Pralet, Cédric 1 Ramakrishnan, C. R. 1 Revol, Nathalie 1 Rueher, Michel 1 Ruiz de Angulo, Vicente 1 Saubion, Frédéric 1 Schichl, Hermann 1 Scott, Joseph K. 1 Skjäl, Anders 1 Smolka, Scott A. 1 Suda, Koki 1 Thabet, Rihab El Houda 1 Videau, Gaétan 1 Vyawahare, Vishwesh A. 1 Watson, Harry A. J. 1 Wechsung, Achim 1 Westerlund, Tapio 1 Xia, Songtao 1 Zoeteweij, Peter all top 5 Cited in 22 Serials 7 Constraints 5 Journal of Global Optimization 3 Artificial Intelligence 2 ACM Transactions on Mathematical Software 2 Automatica 2 Journal of Automated Reasoning 2 European Journal of Operational Research 2 Annals of Mathematics and Artificial Intelligence 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 SIAM Journal on Numerical Analysis 1 Theoretical Computer Science 1 Numerical Algorithms 1 Formal Methods in System Design 1 The Journal of Artificial Intelligence Research (JAIR) 1 INFORMS Journal on Computing 1 Nonlinear Dynamics 1 Communications in Nonlinear Science and Numerical Simulation 1 4OR 1 Journal of Control Theory and Applications 1 Applied and Computational Mathematics all top 5 Cited in 8 Fields 24 Computer science (68-XX) 20 Operations research, mathematical programming (90-XX) 19 Numerical analysis (65-XX) 4 Systems theory; control (93-XX) 2 Mathematical logic and foundations (03-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year