An Overview On Bilevel Programming

This paper contains a bibliography of all references central to bilevel programming that the authors know of. To classify some of the references in this review a short overview of some past research in bilevel program- ming is included. In this bibliography main directions of research as well as main fields of applications and some related methods for solving bilevel programming problems are summarized. We hope this survey facilitates and encourages the research of those who are interested in but unfamiliar with the references in this field. Introduction- A large number of mathematical programming problems have an optimization problem in their constraints. Arising from such a situation is a bilevel programming problem. These problems differ from ordinary optimization problems, as it has two levels of optimization tasks, the upper level or outer optimization task and the lower level or inner optimization task. The lower level optimization task appears as a constraint to the upper level op- timization task, such that only a global optimal solution to the lower level problem may be a feasible candidate to the upper level optimization problem. This caveat makes bilevel optimi- zation a challenging task, which demands immense computa- tional resources to successfully solve even smaller instances of the problem. Motivation- A hierarchical structure appears naturally in many occurrences of decision making, and so bilevel programmes can be applied to many areas of optimisation. Thes are commonly found in many practical problems appearing in transportation (network de- sign, optimal pricing), economics (Stackelberg games, principal- agent problem, taxation, policy decisions), management (net- work facility location, coordination of multi-divisional firms), engineering (optimal design, optimal chemical equilibria) etc.