ICOS: a branch and bound based solver for rigorous global optimization This article describes a software package called Interval Constraint Solver (ICOS), which implements a branch and bound algorithm for rigorously solving global optimization problems. The ICOS library contains algorithms coming from constraint programming, interval analysis, and linear relaxation techniques. It contains an interface to linear programming solvers and local optimization solvers (e.g. Coin/Clp, Cplex, and IpOpt). ICOS has also its own AMPL parser, which enables calling ICOS binary code in a Unix-like command. The ICOS strategy language enables combining and parameterizing existing algorithms for solving optimization problems. Thus, the user can develop his own solving strategies without changing anything in the ICOS internal architecture. Various examples are given to show how the strategy language can be used. We give an overview of ICOS design, implementation, and a quick user’s guide.

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  1. Puranik, Yash; Sahinidis, Nikolaos V.: Domain reduction techniques for global NLP and MINLP optimization (2017)
  2. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  3. Bagnara, Roberto; Carlier, Matthieu; Gori, Roberta; Gotlieb, Arnaud: Exploiting binary floating-point representations for constraint propagation (2016)
  4. Domes, Ferenc; Neumaier, Arnold: Rigorous filtering using linear relaxations (2012)
  5. Pedamallu, Chandra Sekhar; Ozdamar, Linet: Solving kinematics problems by efficient interval partitioning (2011)
  6. Domes, Ferenc; Neumaier, Arnold: Constraint propagation on quadratic constraints (2010)
  7. Lebbah, Y.: ICOS: a branch and bound based solver for rigorous global optimization (2009)
  8. Sahinidis, Nikolaos V.: Global optimization (2009)
  9. Vu, Xuan-Ha; Sam-Haroud, Djamila; Faltings, Boi: Enhancing numerical constraint propagation using multiple inclusion representations (2009)
  10. Vu, Xuan-Ha; Schichl, Hermann; Sam-Haroud, Djamila: Interval propagation and search on directed acyclic graphs for numerical constraint solving (2009)
  11. Wang, Wei; Ghate, Archis; Zabinsky, Zelda B.: Adaptive parameterized improving hit-and-run for global optimization (2009)
  12. Jansson, Christian; Chaykin, Denis; Keil, Christian: Rigorous error bounds for the optimal value in semidefinite programming (2008)
  13. Pedamallu, Chandra Sekhar; Ozdamar, Linet; Ceberio, Martine: Efficient interval partitioning-local search collaboration for constraint satisfaction (2008)
  14. Neumaier, Arnold; Shcherbina, Oleg; Huyer, Waltraud; Vinkó, Tamás: A comparison of complete global optimization solvers (2005)