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Thin and heavy tails in stochastic programming
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SYSNO ASEP 0447994 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Thin and heavy tails in stochastic programming Author(s) Kaňková, Vlasta (UTIA-B) RID
Houda, Michal (UTIA-B) ORCIDSource Title Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 51, č. 3 (2015), s. 433-456Number of pages 24 s. Publication form Print - P Language eng - English Country CZ - Czech Republic Keywords stochastic programming problems ; stability ; Wasserstein metric ; L1 norm ; Lipschitz property ; empirical estimates ; convergence rate ; linear and nonlinear dependence ; probability and risk constraints ; stochastic dominance Subject RIV BB - Applied Statistics, Operational Research R&D Projects GA13-14445S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000361266300005 EID SCOPUS 84940041736 DOI 10.14736/kyb-2015-3-0433 Annotation Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the underlying probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the basis of data. Stochastic estimates of an optimal value and an optimal solution can only be obtained using this approach. Properties of these estimates have been investigated many times. In this paper we intend to study one-stage problems under unusual (corresponding to reality, however) assumptions. In particular, we try to compare the achieved results under the assumptions of thin and heavy tails in the case of problems with linear and nonlinear dependence on the probability measure, problems with probability and risk measure constraints, and the case of stochastic dominance constraints. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2016
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