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Search schemes for random optimization algorithms that preserve the asymptotic distribution

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Chang C. Y. Dorea  and
Cátia R. Gonçalves
Chang C. Y. Dorea*
Affiliation:
Universidade de Brasília
Cátia R. Gonçalves*
Affiliation:
Universidade Estadual Paulista
*
∗Postal address: Departamento de Matemática, Universidade de Brasília, Caixa Postal 04322, 70910–900 Brasília, Brasil. Email address: [email protected]
∗∗Postal address: Departmento de Matemática, Universidade Estadual Paulista, 19060–900 Presdidente Prudente, Saō Paulo, Brasil. Research partially supported by CNPq-Brazil.
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Abstract

Markovian algorithms for estimating the global maximum or minimum of real valued functions defined on some domain Ω ⊂ ℝd are presented. Conditions on the search schemes that preserve the asymptotic distribution are derived. Global and local search schemes satisfying these conditions are analysed and shown to yield sharper confidence intervals when compared to the i.i.d. case.

Keywords

Random search algorithmsglobal optimizationsearch schemesasymptotic distribution

MSC classification

Primary: 65K99: None of the above, but in this section 60G70: Extreme value theory; extremal processes
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 825 - 836
Copyright
Copyright © Applied Probability Trust 1999 

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References

Boender, G. Rinnoy Kan, A., Stougie, L., and Timmer, G. (1982). A stochastic method for global optimization. Math. Prog. 22, 125–140.CrossRefGoogle Scholar
Dekkers, A., and Aarts, E. (1991). Global optimization and simulated annealing. Math. Prog. 50, 367–393.CrossRefGoogle Scholar
Devroye, L. (1978). Progressive global random search of continuous function. Math. Prog. 15, 330–342.CrossRefGoogle Scholar
Dorea, C. C. Y. (1986). Limiting distribution for random optimization method. SIAM: J. Control Optim. 24, 76–82.Google Scholar
Dorea, C. C. Y. (1987). Estimation of the extreme value and the extreme points. Ann. Inst. Statist. Math. 39, 37–48.CrossRefGoogle Scholar
Dorea, C. C. Y. (1990). Stopping rules for a random optimization method. SIAM: J. Control Optim. 28, 841–850.Google Scholar
Dorea, C. C. Y., and Miazaki, E. S. (1992). Parameter free limiting distribution for a random optimization algorithm. Comput. Statist. Data Anal. 14, 391–399.CrossRefGoogle Scholar
Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
Gonçalves, C. R. (1995). Algoritmos de Busca Aleatória para Otimização Global : Estratégias de Busca que Preservam a Distribuição Assintótica, , Departamento de Matemática, Universidade de Brasilia, Brasil.Google Scholar
de Haan, L. (1981). Estimation of the minimum of a function using order statistics. J. Amer. Statist. Assoc. 79, 467–469.CrossRefGoogle Scholar
Leadbetter, M. R., Lindgreen, G. and Rootzén, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.CrossRefGoogle Scholar
Palosaari, S. M., Parviaienen, S. Hüronen, J., Reunanen, J., and Neittaanmaki, P. (1986). A random search algorithm for constrained global optimization. Acta Polytech. Scand. Chem. Technol. Metall. Ser. 172, 1–43.Google Scholar
Resnick, S. J. (1987). Extreme Values, Regular Variation and Point Processes. Springer, Berlin.CrossRefGoogle Scholar
RinnooyKan, A. H. G., and Timmer, G. T. (1987). Stochastic global optimization methods I: clustering methods. Math. Prog. 39, 27–56.CrossRefGoogle Scholar
Solis, F. J., and Wets, R. J. B. (1981). Minimization by random search techiniques. Math. Operat. Res. 6, 19–30.CrossRefGoogle Scholar
Weissman, I. (1981). Confidence intervals for the threshold parameter. Commun. Statist.: Theory Meth. 10, 549–557.CrossRefGoogle Scholar
Weissman, I. (1982). Confidence intervals for the threshold parameter II: unknown shape parameter. Commun. Statist.: Theory Meth. 11, 2451–2474.CrossRefGoogle Scholar
Zhigljavsky, A. A. (1991). Theory of Global Random Search. Kluwer, Dordrecht.CrossRefGoogle Scholar