Risk-Averse Models in Bilevel Stochastic Linear Programming

Burtscheidt, Johanna; Claus, Matthias; Dempe, Stephan

doi:10.48550/arxiv.1901.11349

Cited by 1 publication

(6 citation statements)

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“…For specific risk measures, sufficient conditions for differentiability of Q R have been investigated in [30].…”

Section: Continuity and Differentiabilitymentioning

confidence: 99%

“…Remark 2.16. Theorems 3.7, 3.8 and 3.9 in [30] provide more involved sufficient conditions for continuous differentiability of Q E , Q EE 1 η and Q SD 1 ρ that do not require µ Z to be absolutely continuous.…”

Section: Continuity and Differentiabilitymentioning

confidence: 99%

“…We shall follow the approach of [30], [21] and [34] and confine the stability analysis to locally uniformly • p -integrating sets. A detailed discussion of locally uniformly • p -integrating sets and their generalizations is provided in [20], [35], [36], and [37].…”

Section: Stabilitymentioning

confidence: 99%

“…ρ , CVaR α }, we refer to [30,Section 5]. For the excess probability, the first of the considered quantile-based risk measures, we have EP η…”

Section: Finite Discrete Distributionsmentioning

confidence: 99%

“…More details as well as statements on the coincidence of optimal values and the existence of local and global minimizers are given in [30,Sect. 6 ).…”

Section: Solution Approachesmentioning

confidence: 99%

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Bilevel Optimization under Uncertainty

Burtscheidt¹,

Claus²

2019

Preprint

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We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a hereand-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.

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“…For specific risk measures, sufficient conditions for differentiability of Q R have been investigated in [30].…”

Section: Continuity and Differentiabilitymentioning

confidence: 99%

Section: Continuity and Differentiabilitymentioning

confidence: 99%

Section: Stabilitymentioning

confidence: 99%

“…ρ , CVaR α }, we refer to [30,Section 5]. For the excess probability, the first of the considered quantile-based risk measures, we have EP η…”

Section: Finite Discrete Distributionsmentioning

confidence: 99%

“…More details as well as statements on the coincidence of optimal values and the existence of local and global minimizers are given in [30,Sect. 6 ).…”

Section: Solution Approachesmentioning

confidence: 99%

See 3 more Smart Citations