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Approximative solutions of stochastic optimization problem

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    0348335 - ÚTIA 2011 RIV CZ eng J - Journal Article
    Lachout, Petr
    Approximative solutions of stochastic optimization problem.
    Kybernetika. Roč. 46, č. 3 (2010), s. 513-523. ISSN 0023-5954
    R&D Projects: GA ČR GA201/08/0539
    Institutional research plan: CEZ:AV0Z10750506
    Keywords : Stochastic optimization problem * sensitivity * approximative solution
    Subject RIV: BA - General Mathematics
    Impact factor: 0.461, year: 2010 solutions of stochastic optimization problem.pdf

    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.
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