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

Niels van der Laan, Ward Romeijnders, Maarten H. van der Vlerk

OnderzoeksoutputAcademicpeer review

1 Citaat (Scopus)
165 Downloads (Pure)

Samenvatting

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.
Originele taal-2English
Pagina's (van-tot)325-349
TijdschriftComputational Management Science
Volume15
Nummer van het tijdschrift3-4
Vroegere onlinedatum17-mei-2018
DOI's
StatusPublished - okt-2018

Citeer dit