David Salas Classic linear bilevel optimization assumes that the upper-level decision impacts only the right-hand side of the lower-level constraints, which guarantees a solution under mild conditions. We study existence of solutions for linear bilevel problems with rotations (LBPR, for short), i.e., problems for which the upper-level decision modifies the left-hand side coefficients of the linear follower … Read more
For more than 20 years, single-leader multi-follower (SLMF) problems have been treated as a more difficult class of problems in comparison to bilevel optimization. In this work we challenge this common belief, studying whether SLMF problems can be reformulated as equivalent bilevel optimization problems. We consider both optimistic and pessimistic formulations. For the optimistic case … Read more
It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive … Read more