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

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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.
Original languageEnglish
Pages (from-to)325-349
JournalComputational Management Science
Volume15
Issue number3-4
Early online date17-May-2018
DOIs
Publication statusPublished - Oct-2018

Keywords

  • Stochastic integer programming
  • Convex approximations
  • Error bounds
  • CONVEX APPROXIMATIONS
  • DECOMPOSITION ALGORITHMS
  • PROGRAMS
  • MODELS

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