Guaranteed Bounds for General Nondiscrete Multistage Risk-Averse Stochastic Optimization Programs
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| Názov: | Guaranteed Bounds for General Nondiscrete Multistage Risk-Averse Stochastic Optimization Programs |
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| Autori: | Francesca Maggioni, Georg Ch. Pflug |
| Zdroj: | SIAM Journal on Optimization. 29:454-483 |
| Informácie o vydavateľovi: | Society for Industrial & Applied Mathematics (SIAM), 2019. |
| Rok vydania: | 2019 |
| Predmety: | 101016 Optimisation, 0211 other engineering and technologies, 02 engineering and technology, Risk measures, 01 natural sciences, 101015 Operations Research, Barycentric approximations, First-order stochastic dominance, Bounds, 101015 Operations research, Convex stochastic dominance, 0101 mathematics, 101016 Optimierung, Multistage stochastic programs |
| Popis: | In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such “infinite” problems are practically impossible to solve as they are formulated, and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e., finite tree models, for which the optimal values give upper and lower bounds for the optimal value of the original infinite problem. Typically, there is a gap between the two bounds. However, this gap can be made arbitrarily small by making the approximating trees bushier. We consider approximations in the first-order stochastic sense, in the convex-order sense, and based on subgradient approximations. Their use is shown in a multistage risk-averse production problem. |
| Druh dokumentu: | Article |
| Popis súboru: | text |
| Jazyk: | English |
| ISSN: | 1095-7189 1052-6234 |
| DOI: | 10.1137/17m1140601 |
| Prístupová URL adresa: | http://pure.iiasa.ac.at/id/eprint/15767/1/10.1137%4017M1140601.pdf http://pure.iiasa.ac.at/id/eprint/15767/ https://dblp.uni-trier.de/db/journals/siamjo/siamjo29.html#MaggioniP19 https://aisberg.unibg.it/handle/10446/134539 https://epubs.siam.org/doi/pdf/10.1137/17M1140601 http://pure.iiasa.ac.at/id/eprint/15767/ |
| Rights: | CC BY NC |
| Prístupové číslo: | edsair.doi.dedup.....956b31511d30f18ba66d4a8ac27558ad |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such “infinite” problems are practically impossible to solve as they are formulated, and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e., finite tree models, for which the optimal values give upper and lower bounds for the optimal value of the original infinite problem. Typically, there is a gap between the two bounds. However, this gap can be made arbitrarily small by making the approximating trees bushier. We consider approximations in the first-order stochastic sense, in the convex-order sense, and based on subgradient approximations. Their use is shown in a multistage risk-averse production problem. |
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| ISSN: | 10957189 10526234 |
| DOI: | 10.1137/17m1140601 |