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Title: Approximative solutions of stochastic optimization problems (English)
Author: Lachout, Petr
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 46
Issue: 3
Year: 2010
Pages: 513-523
Summary lang: English
Category: math
Summary: The aim of this paper is to present some ideas how to relax the notion of the optimal solution of the stochastic optimization problem. In the deterministic case, $\varepsilon$-minimal solutions and level-minimal solutions are considered as desired relaxations. We call them approximative solutions and we introduce some possibilities how to combine them with randomness. Relations among random versions of approximative solutions and their consistency are presented in this paper. No measurability is assumed, therefore, treatment convenient for nonmeasurable objects is employed. (English)
Keyword: the optimal solution
Keyword: $\varepsilon $-minimal solutions
Keyword: level-minimal solutions
Keyword: randomness
MSC: 60F99
MSC: 62F12
MSC: 90C15
MSC: 90C31
idZBL: Zbl 1229.90110
idMR: MR2676087
Date available: 2010-09-13T17:01:29Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] Lachout, P.: Stability of stochastic optimization problem – nonmeasurable case.Kybernetika 44 (2008), 2, 259–276. MR 2428223
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Reference: [3] Lachout, P., Liebscher, E., Vogel, S.: Strong convergence of estimators as $\varepsilon _n$-minimizers of optimization problems.Ann. Inst. Statist. Math. 57 (2005), 2, 291–313. MR 2160652, 10.1007/BF02507027
Reference: [4] Lachout, P., Vogel, S.: On continuous convergence and epi-convergence of random functions.Part I: Theory and relations. Kybernetika 39 (2003), 1, 75–98. MR 1980125
Reference: [5] Robinson, S. M.: Analysis of sample-path optimization.Math. Oper. Res. 21 (1996), 3, 513–528. Zbl 0868.90087, MR 1403302, 10.1287/moor.21.3.513
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Reference: [8] Vaart, A. W. van der, Wellner, J. A.: Weak Convergence and Empirical Processes.Springer, New York 1996. MR 1385671


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