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Robust optimization with ambiguous stochastic constraints under mean and dispersion information

Krzysztof Postek (k.postek***at***tilburguniversity.edu)
Aharon Ben-Tal (abental***at***ie.technion.ac.il )
Dick den Hertog (d.denhertog***at***tilburguniversity.edu)
Bertrand Melenberg (b.melenberg***at***tilburguniversity.edu)

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

Keywords: robust optimization, ambiguity, stochastic programming, chance constraints

Category 1: Robust Optimization

Citation: CentER Discussion Paper No. 2015-030

Download: [PDF]

Entry Submitted: 06/05/2015
Entry Accepted: 06/05/2015
Entry Last Modified: 01/08/2017

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