# On the solution of monotone nested variational inequalities

arXiv: https://arxiv.org/abs/2105.13463 · HTML: https://mlsanity.com/paper/2105.13463/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2021.

## Built on by (most cited first, 1 of 1)

- [Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities](https://mlsanity.com/paper/2602.13510/) (2026)

## Abstract (arXiv)

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.