We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We give conditions that guarantee the convergence of the proposed method. Moreover, inspired by recent works in the literature, we provide a convergence rate analysis. In particular, for the simple bilevel instance, we are able to obtain enhanced convergence results.
2020, COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, Pages 335-350 (volume: 77)
An explicit Tikhonov algorithm for nested variational inequalities (01a Articolo in rivista)
Lampariello L., Neumann C., Ricci J. M., Sagratella S., Stein O.
Gruppo di ricerca: Continuous Optimization