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 parametrizedrandom variable arising as the upper level outcome depends continuously on the leader's decision w.r.t. any L-p-norm with p is an element of[1, infinity). This entails continuity of the objective function for a class of models involving convex risk measures defined on appropriate L-p-spaces and allows to formulate verifiable sufficient conditions for the existence of optimal solutions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study focuses on bilevel stochastic linear programs with fixed lower level feasible sets and stochastic follower's goal functions. The research shows that the parametrized random variable is continuous with respect to the leader's decision, allowing for the formulation of sufficient conditions for optimal solutions to exist.