Solution algorithms for bilevel optimization problems

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The bilevel optimization problem is a special class of optimization problem having a two-level hierarchical structure. Such structures arise naturally and frequently in many applications when the decision processes in the so-called upper and lower levels are interdependent. Applications of bilevel optimization include and are not limited to transportation, management, chemistry, environmental issues, economics and engineering. However, the bilevel program is very difficult to solve; it is in fact NP-hard, nonconvex and nonsmooth. Moreover, most of the well-known constraint qualifications in optimization theory do not hold. The main goal of this research project is to develop rigorous solution algorithms tailored to optimistic bilevel programs allowing more than one optimal solution in the lower-level problem. The convex and nonconvex cases will be investigated via the KKT and LLVF reformulations, respectively, and both approaches will be compared.