On continuity in risk-averse bilevel stochastic linear programming with random lower level objective function

We study bilevel stochastic linear programs with fixed lower level feasible set and random follower's goal function and show that the parametrized random variable arising as the upper level outcome depends continuously on the leader's decision w.r.t. any Lp-norm with p∈[1,∞). This entails...

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Veröffentlicht in:Operations research letters Jg. 49; H. 3; S. 412 - 417
1. Verfasser: Claus, Matthias
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.05.2021
Schlagworte:
Bilevel stochastic linear programming
Continuity
Existence results
Risk measures
Existence results
Continuity
Risk measures
Bilevel stochastic linear programming
ISSN:0167-6377, 1872-7468
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Zusammenfassung:We study bilevel stochastic linear programs with fixed lower level feasible set and random follower's goal function and show that the parametrized random variable arising as the upper level outcome depends continuously on the leader's decision w.r.t. any Lp-norm with p∈[1,∞). This entails continuity of the objective function for a class of models involving convex risk measures defined on appropriate Lp-spaces and allows to formulate verifiable sufficient conditions for the existence of optimal solutions.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2021.04.007