Bilevel Linear Optimization Under Uncertainty

Johanna Burtscheidt () and Matthias Claus ()
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Johanna Burtscheidt: University of Duisburg-Essen
Matthias Claus: University of Duisburg-Essen

Chapter Chapter 17 in Bilevel Optimization, 2020, pp 485-511 from Springer

Abstract: Abstract We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader’s outcome can be modeled by a random variable, which gives rise to a broad spectrum of models involving coherent or convex risk measures and stochastic dominance constraints. We outline Lipschitzian properties, conditions for existence and optimality, as well as stability results. Moreover, for finite discrete distributions, we discuss the special structure of equivalent deterministic bilevel programs and its potential use to mitigate the curse of dimensionality.

Keywords: Bilevel stochastic programming; Linear; Risk measure; Stability; Differentiability; Deterministic counterpart (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-52119-6_17

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DOI: 10.1007/978-3-030-52119-6_17

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