Displaying similar documents to “On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications”

On continuous convergence and epi-convergence of random functions. Part I: Theory and relations

Silvia Vogel, Petr Lachout (2003)

Kybernetika

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Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic...

Empirical estimates in stochastic optimization via distribution tails

Vlasta Kaňková (2010)

Kybernetika

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“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied...

On convergence of the empirical mean method for non-identically distributed random vectors

E. Gordienko, J. Ruiz de Chávez, E. Zaitseva (2014)

Applicationes Mathematicae

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We consider the following version of the standard problem of empirical estimates in stochastic optimization. We assume that the underlying random vectors are independent and not necessarily identically distributed but that they satisfy a "slow variation" condition in the sense of the definition given in this paper. We show that these assumptions along with the usual restrictions (boundedness and equicontinuity) on a class of functions allow one to use the empirical mean method to obtain...