Numerica swMATH ID: 21227 Software Authors: Van Hentenryck, Pascal; Deville, Y.; Michel, L. Description: Numerica: A modeling language for global optimization. Many science and engineering applications require the user to find solutions to systems of nonlinear constraints or to optimize a nonlinear function subject to nonlinear constraints. The field of global optimization is the study of methods to find all solutions to systems of nonlinear constraints and all global optima to optimization problems. Numerica is modeling language for global optimization that makes it possible to state nonlinear problems in a form close to the statements traditionally found in textbooks and scientific papers. The constraint-solving algorithm of Numerica is based on a combination of traditional numerical methods such as interval and local methods, and constraint satisfaction techniques.This comprehensive presentation of Numerica describes its design, functions, and implementation. It also discusses how to use Numerica effectively to solve practical problems and reports a number of experimental results.A commercial implementation of Numerica is available from ILOG under the name ILOG Numerica. Homepage: http://www.sciencedirect.com/science/article/pii/S0004370298000538 Related Software: INTOPT_90; RealPaver; BARON; IbexOpt; GlobSol; COCONUT; IBEX; INTBIS; gaol; ICOS; PROFIL/BIAS; CPLEX; ANTIGONE; GLOPT; SeDuMi; AMPL; CHIP; Cosy; Oz; INTLAB Cited in: 49 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A gentle introduction to Numerica. Zbl 0910.68095Van Hentenryck, Pascal 1998 all top 5 Cited by 61 Authors 11 Van Hentenryck, Pascal 8 Jaulin, Luc 4 Chabert, Gilles 4 Deville, Yves 4 Kearfott, Baker 4 Neveu, Bertrand 4 Trombettoni, Gilles 3 Araya, Ignacio J. 3 Goldsztejn, Alexandre 3 Janssen, Micha 3 Jermann, Christophe 3 Michel, Laurent 2 Granvilliers, Laurent 2 Lebbah, Yahia 2 Martin, Benjamin T. 2 Neumaier, Arnold 2 Ozdamar, Linet 2 Pedamallu, Chandra Sekhar 2 Rueher, Michel 1 Apt, Krzysztof Rafal 1 Bergenti, Federico 1 Borradaile, Glencora 1 Ceberio, Martine 1 Collavizza, Hélène 1 Corliss, George F. 1 Correia, Marco 1 Cruz, Jorge T. M. 1 Dal Palù, Alessandro 1 de la Gorce, Martin 1 De Schreye, Danny 1 Desrochers, Benoît 1 Domes, Ferenc 1 Foley, Christopher N. 1 Hansen, Pierre 1 Henrion, Didier 1 Ishii, Daisuke 1 Jansson, Christian 1 Le Bars, Fabrice Abstract 1 Lhomme, Olivier 1 Linderoth, Jeff T. 1 Maher, Michael J. 1 Marendet, Antoine 1 Markót, Mihály Csaba 1 Messine, Frédéric 1 Michel, Claude 1 Monasse, Pascal 1 Ninin, Jordan 1 Puig, Vicenç 1 Puranik, Yash 1 Quevedo, Joseba 1 Reyes, Victor 1 Reynet, Olivier 1 Rossi, Gianfranco 1 Sahinidis, Nikolaos V. 1 Saludes, Jordi 1 Saraswat, Vijay A. 1 Schichl, Hermann 1 Serebrenik, Alexander 1 Sliwka, Jan 1 Vanaret, Charlie 1 Zoeteweij, Peter all top 5 Cited in 21 Serials 12 Constraints 7 Journal of Global Optimization 5 Artificial Intelligence 4 Reliable Computing 2 European Journal of Operational Research 2 Mathematical Programming. Series A. Series B 2 INFORMS Journal on Computing 1 Automatica 1 Fuzzy Sets and Systems 1 Journal of Computational and Applied Mathematics 1 SIAM Journal on Numerical Analysis 1 Theoretical Computer Science 1 The Journal of Logic Programming 1 Computers & Operations Research 1 Journal of Automated Reasoning 1 International Journal of Approximate Reasoning 1 Japan Journal of Industrial and Applied Mathematics 1 Optimization Methods & Software 1 Fundamenta Informaticae 1 Optimization and Engineering 1 4OR all top 5 Cited in 10 Fields 28 Operations research, mathematical programming (90-XX) 14 Numerical analysis (65-XX) 14 Computer science (68-XX) 2 Ordinary differential equations (34-XX) 2 Systems theory; control (93-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) Citations by Year