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.
Lampariello, L., Neumann, C., Ricci, J.M., Sagratella, S., & Stein, O. (2020). An explicit Tikhonov algorithm for nested variational inequalities. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 77(2), 335-350.
Titolo: | An explicit Tikhonov algorithm for nested variational inequalities |
Autori: | |
Data di pubblicazione: | 2020 |
Rivista: | |
Citazione: | Lampariello, L., Neumann, C., Ricci, J.M., Sagratella, S., & Stein, O. (2020). An explicit Tikhonov algorithm for nested variational inequalities. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 77(2), 335-350. |
Handle: | http://hdl.handle.net/11590/379358 |
Appare nelle tipologie: | 1.1 Articolo in rivista |