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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Bibliographic Details
Published in:Operations research letters Vol. 49; no. 3; pp. 412 - 417
Main Author: Claus, Matthias
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2021
Subjects:
Bilevel stochastic linear programming
Continuity
Existence results
Risk measures
Existence results
Continuity
Risk measures
Bilevel stochastic linear programming
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary: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