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Multisection in Interval Branch-and-Bound Methods for Global Optimization II. Numerical Tests

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Abstract

We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The results are published in two papers, the first one contains the theoretical investigations on the convergence properties. An extensive numerical study indicates that multisection can substantially improve the efficiency of interval global optimization procedures, and multisection seems to be indispensable in solving hard global optimization problems in a reliable way.

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References

  1. Berner, S. (1995), Ein paralleles Verfahren zur verifizierten globalen Optimierung, Dissertation, Universität Wuppertal.

  2. Berner, S. (1996), New results on verified global optimization, Computing 57, 323-343.

    Google Scholar 

  3. Csallner, A.E., T. Csendes, and M.Cs. Markót: Multisection in Interval Branch-and-Bound Methods for Global Optimization I. Theoretical Results. Accepted for publication 7. Global Opimization.

  4. Csendes, T. and Pintér, J. (1993), The impact of accelerating tools on the interval subdivision algorithm for global optimization, European J. of Operational Research 65, 314-320.

    Google Scholar 

  5. Csendes, T. and Ratz, D. (1997), Subdivision direction selection in interval methods for global optimization, SIAM J. Numerical Analysis 34, 922-938.

    Google Scholar 

  6. Hammer, R., Hocks, M., Kulisch, U., and Ratz, D. (1993), Numerical Toolbox for Verified Computing I., Springer, Berlin.

    Google Scholar 

  7. Hansen, E. (1992), Global optimization using interval analysis, Marcel Dekker, New York.

    Google Scholar 

  8. Knüppel, O. (1993), BIAS — basic interval arithmetic subroutines, Technical Report 93.3, University of Hamburg-Harburg.

  9. Kearfott, R. B. (1995), A FORTRAN-90 Environment for Research and Prototyping of Enclosure Algorithms for Constrained and Unconstrained Nonlinear Equations, ACM Transactions on Mathematical Software 21, 63-78.

    Google Scholar 

  10. Klatte, R., Kulisch, U., Lawo, C., Rauch, M., and Wiethoff, A. (1993), C-XSC — A C++ Class Library for Extended Scientific Computing, Springer, Heidelberg.

    Google Scholar 

  11. Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, Ch. (1992), PASCAL-XSC — Language Reference with Examples, Springer, New York.

    Google Scholar 

  12. Ratschek, H. and Rokne, J. (1993) Interval Methods, In: Horst R. and Pardalos P. M. (eds.): Handbook of Global Optimization, Kluwer, Dordrecht, 751-828.

    Google Scholar 

  13. Ratz, D. (1992), Automatische Ergebnisverifikation bei globalen Optimierungsproblemen. Dissertation, Universität Karlsruhe.

  14. Ratz, D. and Csendes, T. (1995), On the selection of Subdivision Directions in Interval Branch-and-Bound Methods for Global Optimization, J. Global Optimization 7, 183-207.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Informatics, József Attila University, Szeged, Árpád tér 2., Hungary

    Mihály Csaba Markót

  2. Department of Applied Informatics, József Attila University, Szeged, Árpád tér 2., Hungary

    Tibor Csendes

  3. Department of Computer Science, Juhász Gyula Teachers Training College, Szeged, Boldogasszony sgt. 4., Hungary

    András Erik Csallner

Authors
  1. Mihály Csaba Markót
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  2. Tibor Csendes
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  3. András Erik Csallner
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Csaba Markót, M., Csendes, T. & Csallner, A.E. Multisection in Interval Branch-and-Bound Methods for Global Optimization II. Numerical Tests. Journal of Global Optimization 16, 219–228 (2000). https://doi.org/10.1023/A:1008359223042

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  • DOI: https://doi.org/10.1023/A:1008359223042

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