Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information

Krzysztof Postek, A. Ben-Tal, Dick den Hertog, Bertrand Melenberg

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Abstract

In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal and Hochman (1972) in which tight upper and lower bounds on the expectation of a convex function of a random variable are given. We use these bounds to derive
exact robust counterparts of expected feasibility of convex constraints and to construct new safe tractable approximations of chance constraints. Numerical examples show our method to be applicable to numerous applications of Robust Optimization, e.g., where implementation error or linear decision rules are present.
Also, we show that the methodology can be used for optimization the average-case performance of worst-case
optimal Robust Optimization solutions.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages36
Volume2015-030
Publication statusPublished - 5 Jun 2015

Publication series

NameCentER Discussion Paper
Volume2015-030

Keywords

  • robust optimization
  • ambiguity
  • stochastic programming
  • chance constraints

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  • Cite this

    Postek, K., Ben-Tal, A., den Hertog, D., & Melenberg, B. (2015). Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information. (CentER Discussion Paper; Vol. 2015-030). CentER, Center for Economic Research.