On the solution of monotone nested variational inequalities
Optimization and Control
2021-12-20 v2
Abstract
We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in the literature to guarantee the convergence to solutions of the nested variational inequality. Specifically, we only need monotonicity of the upper- and the lower-level variational inequalities. Also, we provide the first complexity analysis for nested variational inequalities considering optimality of both the upper- and lower-level.
Cite
@article{arxiv.2105.13463,
title = {On the solution of monotone nested variational inequalities},
author = {Lorenzo Lampariello and Gianluca Priori and Simone Sagratella},
journal= {arXiv preprint arXiv:2105.13463},
year = {2021}
}