Bilevel optimization, near-optimal variant and application for energy pricing problems
Mathieu Besançon, Ecole Polytechnique de Montréal.
Sala conferenze IMATI-CNR, Pavia – Martedì 26 Marzo 2019 h.15:00
Abstract. Bilevel optimization is a class of mathematical optimization problems with a lower level problem embedded in the constraints. Although they have the direct game-theoretic interpretation as so-called leader-follower or Stackelberg games, they have been used to model various decision-making configurations. Several properties of bilevel problems are developed, including the near-optimal variant, corresponding to the anticipation of a bounded rationality decision-making at the second level, or accepting a given deviation from the optimum. We show that this problem is a generalization of the pessimistic bilevel problem and in particular of a variant introduced by Wiesemann, Tsoukalas, Kleniati, Rustem, 2013, SIAM J. Opt. We derive a solution method for some cases of near-optimal bilevel problems, building on the methodology developed in both bilevel and robust optimization.
In a second part of the presentation, an application of bilevel optimization will be presented for the optimal pricing of a Time-and-Level-of-Use tariff for Demand Response in power systems.