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.

References in zbMATH (referenced in 46 articles , 1 standard article )

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  1. Marendet, Antoine; Goldsztejn, Alexandre; Chabert, Gilles; Jermann, Christophe: A standard branch-and-bound approach for nonlinear semi-infinite problems (2020)
  2. Neveu, Bertrand; de la Gorce, Martin; Monasse, Pascal; Trombettoni, Gilles: A generic interval branch and bound algorithm for parameter estimation (2019)
  3. Desrochers, B.; Jaulin, L.: Thick set inversion (2017)
  4. Martin, Benjamin; Correia, Marco; Cruz, Jorge: A certified branch & bound approach for reliability-based optimization problems (2017)
  5. Martin, Benjamin; Goldsztejn, Alexandre; Granvilliers, Laurent; Jermann, Christophe: Constraint propagation using dominance in interval branch & bound for nonlinear biobjective optimization (2017)
  6. Michel, L.; Van Hentenryck, P.: A microkernel architecture for constraint programming (2017)
  7. Puranik, Yash; Sahinidis, Nikolaos V.: Domain reduction techniques for global NLP and MINLP optimization (2017)
  8. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  9. Jaulin, Luc: Range-only SLAM with indistinguishable landmarks; a constraint programming approach (2016)
  10. Neveu, Bertrand; Trombettoni, Gilles; Araya, Ignacio: Node selection strategies in interval branch and bound algorithms (2016)
  11. Kearfott, Ralph Baker: Some observations on exclusion regions in branch and bound algorithms (2015)
  12. Neveu, Bertrand; Trombettoni, Gilles; Araya, Ignacio: Adaptive constructive interval disjunction: algorithms and experiments (2015)
  13. Ninin, Jordan; Messine, Frédéric; Hansen, Pierre: A reliable affine relaxation method for global optimization (2015)
  14. Schichl, Hermann; Markót, Mihály Csaba; Neumaier, Arnold: Exclusion regions for optimization problems (2014)
  15. Ishii, Daisuke; Goldsztejn, Alexandre; Jermann, Christophe: Interval-based projection method for under-constrained numerical systems (2012)
  16. Le Bars, Fabrice; Sliwka, Jan; Jaulin, Luc; Reynet, Olivier: Set-membership state estimation with fleeting data (2012)
  17. Kearfott, Ralph Baker: Interval computations, rigour and non-rigour in deterministic continuous global optimization (2011)
  18. Pedamallu, Chandra Sekhar; Ozdamar, Linet: Solving kinematics problems by efficient interval partitioning (2011)
  19. Collavizza, Hélène; Rueher, Michel; Van Hentenryck, Pascal: CPBPV: a constraint-programming framework for bounded program verification (2010)
  20. Domes, Ferenc; Neumaier, Arnold: Constraint propagation on quadratic constraints (2010)

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