MPEC Methods for Bilevel Optimization Problems

We study optimistic bilevel optimization problems, where we assume the lower-level problem is convex with a nonempty, compact feasible region and satisfies a constraint qualification for all possible upper-level decisions. Replacing the lowerlevel optimization problem by its first-order conditions results in a mathematical program with equilibrium constraints (MPEC) that needs to be solved. We review the relationship between the MPEC and bilevel optimization problem and then survey the theory, algorithms, and software environments for solving the MPEC formulations.

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