GlobSol: history, composition, and advice on use The GlobSol software package combines various ideas from interval analysis, automatic differentiation, and constraint propagation to provide verified solutions to unconstrained and constrained global optimization problems. After briefly reviewing some of these techniques and GlobSol’s development history, we provide the first overall description of GlobSol’s algorithm. Giving advice on use, we point out strengths and weaknesses in GlobSol’s approaches. Through examples, we show how to configure and use GlobSol.

References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  2. Kearfott, Ralph Baker: Some observations on exclusion regions in branch and bound algorithms (2015)
  3. Ninin, Jordan; Messine, Frédéric; Hansen, Pierre: A reliable affine relaxation method for global optimization (2015)
  4. Kearfott, Ralph Baker: On rigorous upper bounds to a global optimum (2014)
  5. Kearfott, Ralph Baker; Castille, Jessie M.; Tyagi, Gaurav: Assessment of a non-adaptive deterministic global optimization algorithm for problems with low-dimensional non-convex subspaces (2014)
  6. Griewank, Andreas: From the product example to PDE adjoints, algorithmic differentiation and its application (invited talk) (2013)
  7. Kearfott, Ralph Baker; Castille, Jessie; Tyagi, Gaurav: A general framework for convexity analysis in deterministic global optimization (2013)
  8. Kearfott, Ralph Baker; Muniswamy, Sowmya; Wang, Yi; Li, Xinyu; Wang, Qian: On smooth reformulations and direct non-smooth computations for minimax problems (2013)
  9. Gay, David M.: Using expression graphs in optimization algorithms (2012)
  10. Griewank, Andreas: Who invented the reverse mode of differentiation? (2012)
  11. Chevillard, S.; Harrison, J.; Joldeş, M.; Lauter, Ch.: Efficient and accurate computation of upper bounds of approximation errors (2011)
  12. Domes, Ferenc; Neumaier, Arnold: Rigorous enclosures of ellipsoids and directed Cholesky factorizations (2011)
  13. Kearfott, Ralph Baker: Interval computations, rigour and non-rigour in deterministic continuous global optimization (2011)
  14. Kearfott, R. Baker: Erratum: Validated linear relaxations and preprocessing: some experiments (2011)
  15. Nataraj, P.S.V.; Sondur, Shanta: The extrapolated interval global optimization algorithm (2011)
  16. Revol, Nathalie: Standardized interval arithmetic and interval arithmetic used in libraries (2010)
  17. Beelitz, Thomas; Frommer, Andreas; Lang, Bruno; Willems, Paul: A framework for existence tests based on the topological degree and homotopy (2009)
  18. Kearfott, R.Baker: GlobSol user guide (2009)
  19. Nataraj, P.S.V.; Arounassalame, M.: An algorithm for constrained global optimization of multivariate polynomials using the Bernstein form and John optimality conditions (2009)
  20. Pedamallu, Chandra Sekhar; Özdamar, Linet; Csendes, Tibor; Vinkó, Tamás: Efficient interval partitioning for constrained global optimization (2008)

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