Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

Niels Laan (), Ward Romeijnders () and Maarten H. Vlerk
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Niels Laan: University of Groningen
Ward Romeijnders: University of Groningen
Maarten H. Vlerk: University of Groningen

Computational Management Science, 2018, vol. 15, issue 3, No 2, 325-349

Abstract: Abstract 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.

Keywords: Stochastic integer programming; Convex approximations; Error bounds (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10287-018-0315-z

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