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Convergence rate of empirical estimates in stochastic programming. (English) Zbl 0906.90133
Summary: It is well-known that many practical optimization problems with random elements lead from the mathematical point of view to deterministic optimization problems depending on the random elements through probability laws only. Further, it is also well-known that these probability laws are known very seldom. Consequently, statistical estimates of the unknown probability measure, if they exist, must be employed to obtain some estimates of the optimal value and the optimal solution, at least.
If the theoretical distribution function is completely unknown then an empirical distribution usually substitutes it. Great attention has been already paid to the studying of statistical properties of such empirical estimates in the literature. The aim of this paper is to discuss the convergence rate.

MSC:
90C15 Stochastic programming
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