Multilevel optimization: A mathematical programming perspective

Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which have often existed in practice. Similarly, tractable game-theoretic approaches have not allowed for a continuous solution space in which one player´s decision restricts the feasible region of another. This paper offers a formulation to help model this type of decision making hierarchy. In addition, characterizations and algorithmic approaches are discussed. The ultimate purpose of this paper is to motivate wider interest in the areas of both modelling and solution strategies for this large class of nonconvex programming problems.