A Branch-and-Bound method for semivectorial bilevel problems Seminar

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In semivectorial bilevel optimization one considers an optimization problem, the upper-level problem, which contains a solution set of a multiobjective optimization problem, the lower-level problem, as a constraint. Within this talk, we follow the optimistic approach, i.e., we choose the weakly efficient points of the lower-level problem that are most suitable for the upper-level objective function. As a next step, we replace the weak efficiency map of the lower-level problem by using its optimal value function and obtain the so-called value function reformulation. Based on that, we present a global solver for optimistic semivectorial bilevel problems. The proposed branch-and-bound method refines suitable partitions until the approximations of the value function, and thus the lower and upper bound on the minimal value, are sufficiently close