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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Vydáno v:Operations research letters Ročník 49; číslo 3; s. 412 - 417
Hlavní autor: Claus, Matthias
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.05.2021
Témata:
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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Shrnutí: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