11. May 2023, 15:00 until 16:30
AKOR Seminar: David Salas, Universidad de O’Higgins
Bayesian approach and polyhedral geometry of stochastic linear bilevel programming

Abstract: In this talk we will review some recent results on the Bayesian approach for bilevel programming. We focus our attention in linear bilevel programming and the beliefs induced by uncertain lower-level costs. We show that such problems (and their sample average approximations) can be written as piecewise linear minimization problems over a polyhedral complex induced by the feasible region of the bilevel formulation. We will describe two algorithms to solve the problem: a deterministic one based on vertex enumeration, and a Monte-Carlo algorithm based on sampling full-dimensional elements of the aforementioned polyhedral complex.