GlobSol: History, Composition, and Advice on Use

  • R. Baker Kearfott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2861)


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.


Verified global optimization interval analysis GlobSol constraint propagation automatic differentiation 


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  1. 1.
    Berz, M., Bischof, C., Corliss, G., Griewank, A. (eds.): Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia (1996)zbMATHGoogle Scholar
  2. 2.
    Corliss, G., Faure, C., Griewank, A., Hascoët, L., Naumann, U. (eds.): Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer, NewYork (2002)zbMATHGoogle Scholar
  3. 3.
    Corliss, G.F., Kearfott, R.B.: Rigorous global search: Industrial applications. In: Developments in Reliable Computing, pp. 1–16. Kluwer, Dordrecht (2000)Google Scholar
  4. 4.
    Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Least Squares. Prentice-Hall, Englewood Cliffs (1983)Google Scholar
  5. 5.
    Gau, C.-Y., Stadtherr, M.A.: Nonlinear parameter estimation using interval analysis. AIChE Symp. Ser. 94(304), 445–450 (1999)Google Scholar
  6. 6.
    Gill, P.E., Murray, W., Wright, M.: Practical Optimization. Academic Press, New York (1981)zbMATHGoogle Scholar
  7. 7.
    Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Frontiers in Applied Mathematics. SIAM, Philadelphia (2000)zbMATHGoogle Scholar
  8. 8.
    Griewank, A.: ADOL-C, a package for automatic differentiation of algorithms written in C/C++ (2002),
  9. 9.
    Griewank, A., Corliss, G.F. (eds.): Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia (1991)zbMATHGoogle Scholar
  10. 10.
    Hansen, E.R.: Global Optimization Using Interval Analysis. Marcel Dekker, Inc., New York (1992)zbMATHGoogle Scholar
  11. 11.
    Hoefkens, J.: Rigorous Numerical Analysis with High-Order Taylor Models. PhD thesis, Department of Mathematics, Michigan State University (2001)Google Scholar
  12. 12.
    Kearfott, R.B.: Abstract generalized bisection and a cost bound. Math. Comp. 49(179), 187–202 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kearfott, R.B.: Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems. Computing 47(2), 169–191 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kearfott, R.B.: An interval branch and bound algorithm for bound constrained optimization problems. Journal of Global Optimization 2, 259–280 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kearfott, R.B.: Algorithm 763: INTERVAL ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22(4), 385–392 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)zbMATHGoogle Scholar
  17. 17.
    Kearfott, R.B.: Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear algebraic systems. SIAM J. Sci. Comput. 18(2), 574–594 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kearfott, R.B.: On proving existence of feasible points in equality constrained optimization problems. Math. Prog. 83(1), 89–100 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kearfott, R.B.: Interval analysis: Interval Newton methods. In: Encyclopedia of Optimization, vol. 3, pp. 76–78. Kluwer, Dordrecht (2001)Google Scholar
  20. 20.
    Kearfott, R.B., Dawande, M., Du, K.-S., Hu, C.-Y.: Algorithm 737: INTLIB, a portable FORTRAN 77 interval standard function library. ACM Trans. Math. Software 20(4), 447–459 (1994)zbMATHCrossRefGoogle Scholar
  21. 21.
    Kearfott, R.B., Dian, J.: An iterative method for finding approximate feasible points (1998) (preprint),
  22. 22.
    Kearfott, R.B., Novoa, M.: Algorithm 681: INTBIS, a portable interval Newton/ bisection package. ACM Trans. Math. Software 16(2), 152–157 (1990)zbMATHCrossRefGoogle Scholar
  23. 23.
    Kearfott, R.B.: Walster G.W. Symbolic preconditioning with Taylor models: Some examples (2001) (accepted for publication in reliable computing)Google Scholar
  24. 24.
    Kearfott, R.B., Walster, G.W.: On stopping criteria in verified nonlinear systems or optimization algorithms. ACM Trans. Math. Software 26(3), 373–389 (2000)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Lemaréchal, C.: Nondifferentiable optimization. In: Powell, M.J.D. (ed.) Nonlinear Optimization 1981, pp. 85–89. Academic Press, New York (1982)Google Scholar
  26. 26.
    Morgan, A.P.: Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems. Prentice-Hall, Englewood Cliffs (1987)zbMATHGoogle Scholar
  27. 27.
    Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)zbMATHGoogle Scholar
  28. 28.
    Rall, L.B.: Automatic Differentiation: Techniques and Applications. In: Rall, L.B. (ed.) Automatic Differentiation. LNCS, vol. 120, Springer, Heidelberg (1981)Google Scholar
  29. 29.
    Ratz, D., Csendes, T.: On the selection of subdivision directions in interval branch-and-bound methods for global optimization. J. Global Optim. 7, 183–207 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Schnepper, C.A.: Large Grained Parallelism in Equation-Based Flowsheeting Using Interval Newton / Generalized Bisection Techniques. PhD thesis, University of Illinois, Urbana (1992)Google Scholar
  31. 31.
    Van Hentenryck, P., Michel, L., Deville, Y.: Numerica: A Modeling Language for Global Optimization. MITPress, Cambridge (1997)Google Scholar
  32. 32.
    Van Iwaarden, R.J.: An Improved Unconstrained Global Optimization Algorithm. PhD thesis, University of Colorado at Denver (1996)Google Scholar
  33. 33.
    Yang, J., Kearfott, R.B.: Interval linear and nonlinear regression: New paradigms, implementations, and experiments, or new ways of thinking about data fitting (2002), available at

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • R. Baker Kearfott
    • 1
  1. 1.Department of MathematicsUniversity of Louisiana at LafayetteLafayetteUSA

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