Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations
| Autor: | Maarten H. van der Vlerk, Niels van der Laan, Ward Romeijnders |
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| Přispěvatelé: | Research programme OPERA |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
021103 operations research Hierarchy (mathematics) Approximations of π MODELS 0211 other engineering and technologies Regular polygon Probability density function DECOMPOSITION ALGORITHMS 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Management Information Systems Periodic function Error bounds CONVEX APPROXIMATIONS PROGRAMS Simple (abstract algebra) Stochastic integer programming Order (group theory) 0101 mathematics Information Systems Mathematics Integer (computer science) |
| Zdroj: | Computational Management Science, 15(3-4), 325-349. SPRINGER HEIDELBERG |
| ISSN: | 1619-6988 1619-697X |
| DOI: | 10.1007/s10287-018-0315-z |
| Popis: | We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3-46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables. |
| Databáze: | OpenAIRE |
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