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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Al-Mharmah, H. and Calvin, J. (1996), Optimal random non-adaptive algorithm for optimization of Brownian motion, Journal of Global Optimization 8: 81–90.
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.
Billingsley, P. (1968), Convergence of Probability Measures, Wiley, New York.
Calvin, J. (1995), Average performance of passive algorithms for global optimization, J. Math. Anal. Appl. 191: 608–617.
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.
Calvin, J. (1997), Average performance of a class of adaptive algorithms for global optimization, The Annals of Applied Prob. 7: 711–730.
Feller, W. (1971), An Introduction to Probability Theory and Its Applications, II, Wiley, New York.
Fitzsimmons, P. J., Pitman, J. W. and Yor, M. (1992), Markovian bridges: Construction, Palm interpretation, and Splicing, Sem. Stochastic Processes, Birkhäuser, Boston.
Imhof, J. P. (1984), Density factorization for Brownian motion, meander and the threedimensional Bessel process, and applications, J. Appl. Prob. 21: 500–510.
Ritter, K. (1990), Approximation and optimization on the Wiener space, J. Complexity 6: 337–364.
Revuz, D. and M. Yor (1991), Continuous Martingales and Brownian Motion, Springer Verlag, Berlin/New York.
Karlin, S. and Taylor, H. (1975), A First Course in Stochastic Processes, Academic Press, New York.
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.
Williams, D. (1974), Path decomposition and continuity of local time for one-dimensional diffusions, I, Proc. London Math. Soc., Ser. 3 28: 738–68.
Zhigljavsky, A. (1991), Theory of Global Random Search, Kluwer Academic Publishers, Dordrecht/Boston/London.
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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