Abstract
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.
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This work was supported by the MIUR-DAAD Joint Mobility Program under Grant 34793 and Project-ID 57396680.
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Lampariello, L., Neumann, C., Ricci, J.M. et al. An explicit Tikhonov algorithm for nested variational inequalities. Comput Optim Appl 77, 335–350 (2020). https://doi.org/10.1007/s10589-020-00210-1
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DOI: https://doi.org/10.1007/s10589-020-00210-1