Hierarchical Optimization

Hoang Tuy

ABSTRACT

Hierarchical optimization deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. The most important case is the bilevel linear programming problem (BLP), which has attracted much attention from researchers due to numerous applications in various fields. Basic properties of BLP, together with solution methods proposed so far in the literature, are discussed, based on different reformulations of BLP as a single mathematical program. In particular, a branch-andbound method is described in detail. The relation of BLP with multicriteria optimization is clarified, and the current research situation in nonlinear bilevel programming is briefly reviewed.