Abstract
Let us consider a stochastic optimization problem in which the optimum is sought with respect to the mathematical expectation. Assume the probability laws of the random variables to be unknown. Some estimates of the optimal solution and the optimal value of the optimalized function were given in [3]. These estimates were obtained using realizations of random variables having the same probability laws as those in the problem. In this paper we are going deeper in this direction. We investigate the rate of convergence for these estimates, It is shown that this rate is at least exponencial.
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References
Dupačová J. (1976): Experience: in Stochastic Programming Models. IX International Symposium on Mathematical Programming, Budapest 1976
Hoeffding W. (1963): Probability Inequalities for Sums of Bounded Random Variables. Journal of the Americ. Statist. Ass. 58 (1963), No. 301, 13–30.
Kaňková V. (1974): Optimum Solution of a Stochastic Optimization Problem with Unknown Parameters. In: Trans, of the Seventh Prague Conference, Prague 1974, Academia, Prague 1978.
Rockafellar R. (1970): Convex Analysis, Princeton Press New Jersey 1970
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© 1978 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Kaňková, V. (1978). An Approximative Solution of a Stochastic Optimization Problem. In: Transactions of the Eighth Prague Conference. Czechoslovak Academy of Sciences, vol 8A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9857-5_33
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DOI: https://doi.org/10.1007/978-94-009-9857-5_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9859-9
Online ISBN: 978-94-009-9857-5
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