View this talk here: https://www.youtube.com/watch?v=y5gekUsNlnA&feature=youtu.be

Hierarchical programs are optimization problems whose feasible set is implicitly defined as

the solution set of another, lower-level, problem. As a major departure from the more general bilevel

structures, this talk focuses only on lower-level problems that are non-parametric with respect to the upper

level variables. In particular, the minimization of an objective function over the solution set of a lower-level

variational inequality is considered, which is a special instance of semi-infinite programs and encompasses

simple bilevel problems and selection of Nash equilibria as particular cases. To tackle this hierarchical

problem, a suitable approximated version is introduced. On the one hand, this does not perturb the original

(exact) program too much, on the other hand it allows relying on suitable exact penalty approaches whose

convergence properties are established.

Joint work with Lorenzo Lampariello and Simone Sagratella