Bilevel programming via generalized convexity and variational analysis by Boris Mordukhovich

This talk is devoted to discussing optimistic bilevel programs based on the so-called value/marginal function approach. This approach allows us reducing bilevel programs to single-value problems of mathematical programming with unavoidably nondifferentiable (and often nonconvex) data. Applying generalized differentiation theory of variational analysis in convex and nonconvex settings together with methods of nondifferentiable programming, we derive verifiable optimality conditions for optimistic bilevel programs, which give us the potential for numerical implementations. We also discuss a relatively new class of seminfinite bilevel programs and formulate several open questions of the further research.