joint work with Nikolaos Lappas, Chrysanthos Gounaris
We propose a primal branch-and-bound algorithm that generalizes the well-known cutting plane method of Mutapcic and Boyd to the case of decision-dependent uncertainty sets. A comprehensive computational study showcases the advantages of the proposed algorithm over that of existing methods that rely on classical duality-based reformulations.
joint work with Miguel Anjos, Luce Brotcorne
Bilevel optimization corresponds to integrating the optimal response to a lower-level problem in a problem. We introduce near-optimal robustness for bilevel problems, building on existing concepts from the literature. This model generalizes the pessimistic approach, protecting the decision-maker from limited deviations of the lower level. This models finds intuitive interpretations in various optimization settings modelled as bilevel problems. We develop a duality-based solution method for cases where the lower-level is convex, leveraging the methodology from robust and bilevel optimization.
joint work with Kartikey Sharma
The efficacy of robust optimization spans a variety of settings with predetermined uncertainty sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This talk takes a step towards generalizing robust optimization to problems with decision-dependent uncertainties, which we show are NP-complete. We introduce a class of uncertainty sets whose size depends on decisions, and proposed reformulations that improve upon alternative techniques. In addition, the proactive uncertainty control mitigates over conservatism of current approaches.