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Comparison of One-dimensional Composite and Non-composite Passive Algorithms

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Abstract

In this paper we analyze composite non-adaptive algorithms for optimization of one-dimensional Brownian motion. We show that a composite deterministic algorithm has a better average performance than the best random one.

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References

  1. Al-Mharmah, H. and Calvin, J. (1996), Optimal random non-adaptive algorithm for optimization of Brownian motion, Journal of Global Optimization 8: 81–90.

    Google Scholar 

  2. Asmussen, S., Glynn, P. and Pitman, J. (1995), Discretization error in simulation of onedimensional reflecting Brownian motion, The Annals of Applied Probability 5: 875–896.

    Google Scholar 

  3. Billingsley, P. (1968), Convergence of Probability Measures, Wiley, New York.

  4. Calvin, J. (1995), Average performance of passive algorithms for global optimization, J. Math. Anal. Appl. 191: 608–617.

    Google Scholar 

  5. Calvin, J. (1996), Asymptotically optimal non-adaptive algorithms for minimization of Brownian motion. In The Mathematics of Numerical Analysis (J. Renegar, M. Shub, S. Smale, eds.) American Mathematical Society, Lectures in Applied Mathematics, Vol. 32.

  6. Calvin, J. (1997), Average performance of a class of adaptive algorithms for global optimization, The Annals of Applied Prob. 7: 711–730.

    Google Scholar 

  7. Feller, W. (1971), An Introduction to Probability Theory and Its Applications, II, Wiley, New York.

  8. Fitzsimmons, P. J., Pitman, J. W. and Yor, M. (1992), Markovian bridges: Construction, Palm interpretation, and Splicing, Sem. Stochastic Processes, Birkhäuser, Boston.

  9. Imhof, J. P. (1984), Density factorization for Brownian motion, meander and the threedimensional Bessel process, and applications, J. Appl. Prob. 21: 500–510.

    Google Scholar 

  10. Ritter, K. (1990), Approximation and optimization on the Wiener space, J. Complexity 6: 337–364.

    Google Scholar 

  11. Revuz, D. and M. Yor (1991), Continuous Martingales and Brownian Motion, Springer Verlag, Berlin/New York.

  12. Karlin, S. and Taylor, H. (1975), A First Course in Stochastic Processes, Academic Press, New York.

    Google Scholar 

  13. Shepp, L. A. (1976), The joint density of the maximum and its location for a Wiener process with drift, J. Appl. Prob. 16: 423–427.

    Google Scholar 

  14. Williams, D. (1974), Path decomposition and continuity of local time for one-dimensional diffusions, I, Proc. London Math. Soc., Ser. 3 28: 738–68.

    Google Scholar 

  15. Zhigljavsky, A. (1991), Theory of Global Random Search, Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

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Authors and Affiliations

  1. Industrial Engineering Department, University of Jordan, Amman, 11942, Jordan

    Hisham A. Al-Mharmah

  2. Department of Computer and Information Science, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    James M. Calvin

Authors
  1. Hisham A. Al-Mharmah
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  2. James M. Calvin
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Al-Mharmah, H.A., Calvin, J.M. Comparison of One-dimensional Composite and Non-composite Passive Algorithms. Journal of Global Optimization 15, 169–180 (1999). https://doi.org/10.1023/A:1008308319157

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  • DOI: https://doi.org/10.1023/A:1008308319157

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