# From resolvents to generalized equations and quasi-variational inequalities: existence and differentiability

arXiv: https://arxiv.org/abs/2109.13569 · HTML: https://mlsanity.com/paper/2109.13569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2021.

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

- [Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems](https://mlsanity.com/paper/2212.07844/) (2022)

## Abstract (arXiv)

We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of both mappings. We demonstrate that the directional differentiability of the solution map can be verified by using the directional differentiability of the single-valued operator and of the resolvent of the set-valued mapping. The result is applied to quasi-generalized equations in which we have an additional dependence of the solution within the set-valued part of the equation.