Abstract
The Stability Index Method (SIM) combines stochastic and deterministic algorithms to find global minima of multidimensional functions. The functions may be nonsmooth and may have multiple local minima. The method examines the change of the diameters of the minimizing sets for its stopping criterion. At first, the algorithm uses the uniform random distribution in the admissible set. Then normal random distributions of decreasing variation are used to focus on probable global minimizers. To test the method, it is applied to seven standard test functions of several variables. The computational results show that the SIM is efficient, reliable and robust.
Similar content being viewed by others
References
Bagirov A.M., Rubinov A.M., Zhang J. (2005), Local optimization method with global multidimensional search. Journal of Global Optimization 32, 161–179
Bornemann F., Laurie D., Wagon S., Waldvogel J. (2004), The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. Society for Industrial and Applied Mathematics, Philadelphia
Brent P. (1973), Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, NJ
Gutman S., Ramm A.G., Scheid W. (2002), Inverse scattering by the stability index method. Journal of Inverse and Ill-Posed Problems 10(N5): 487–502
Kirkpatrick S. (1984), Optimization by simulated annealing: quantitative studies. Journal of Statistical Physics 34, 975–986
Miller R.E. (2000), Optimization: Foundations and Applications. Wiley, New York
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (1992), Numerical Recepies in FORTRAN. Second edition. Cambridge University Press, Cambridge
Ramm A.G., Gutman S. (2005), Optimization methods in direct and inverse scattering. In: Jeyakumar V., Rubinov A.M. (eds). Continuous Optimization: Current Trends and Modern Applications. Springer, New York, pp. 51–110
Yiu K.F.C., Liu Y., Teo K.L. (2004), A hybrid descent method for global optimization. Journal of Global Optimization 28, 229–238
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors thank the referees for valuable suggestions.
Rights and permissions
About this article
Cite this article
Dover, J., Gutman, S. Stability Index Method for Global Minimization. J Glob Optim 36, 307–318 (2006). https://doi.org/10.1007/s10898-006-9010-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9010-7