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Stochastic programming problems with generalized integrated chance constraints
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SYSNO ASEP 0381903 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Stochastic programming problems with generalized integrated chance constraints Author(s) Branda, Martin (UTIA-B) RID, ORCID Number of authors 1 Source Title Optimization. - : Taylor & Francis - ISSN 0233-1934
Roč. 61, č. 8 (2012), s. 949-968Number of pages 22 s. Language eng - English Country DE - Germany Keywords chance constraints ; integrated chance constraints ; penalty functions ; sample approximations ; blending problem Subject RIV BB - Applied Statistics, Operational Research R&D Projects GAP402/10/1610 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000306663000003 DOI https://doi.org/10.1080/02331934.2011.587007 Annotation If the constraints in an optimization problem are dependent on a random parameter, we would like to ensure that they are fulfilled with a high level of reliability. The most natural way is to employ chance constraints. However, the resulting problem is very hard to solve. We propose an alternative formulation of stochastic programs using penalty functions. The expectations of penalties can be left as constraints leading to generalized integrated chance constraints, or incorporated into the objective as a penalty term. We show that the penalty problems are asymptotically equivalent under quite mild conditions. We discuss applications of sample-approximation techniques to the problems with generalized integrated chance constraints and propose rates of convergence for the set of feasible solutions. We will direct our attention to the case when the set of feasible solutions is finite, which can appear in integer programming. The results are then extended to the bounded sets with continuous variables. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2013
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