A bilevel program is a generalization of a standard mathematical program in which we consider a hierarchical decision system with two independent decision makers whose interests are not necessarily aligned. In the first part of the talk, we'll discuss the importance and applications of this class of mathematical programs, including its connection to stochastic integer programming, game theory, and other topics from the literature. In the second part of the talk, we'll introduce the basic theory of bilevel programming, focusing on the general mixed integer case. Finally, we review our efforts to develop algorithms and a solver for general mixed integer bilevel programs.
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