# The resolvent order: a unification of the orders by Zarantonello, by Loewner, and by Moreau

arXiv: https://arxiv.org/abs/1606.08809 · HTML: https://mlsanity.com/paper/1606.08809/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2016.

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

- [PDE-regularized Dynamics-informed Diffusion with Uncertainty-aware Filtering for Long-Horizon Dynamics](https://mlsanity.com/paper/2604.09058/) (2026)

## Abstract (arXiv)

We introduce and investigate the resolvent order, which is a binary relation on the set of firmly nonexpansive mappings. It unifies well-known orders introduced by Loewner (for positive semidefinite matrices) and by Zarantonello (for projectors onto convex cones). A connection with Moreau's order of convex functions is also presented. We also construct partial orders on (quotient sets of) proximal mappings and convex functions. Various examples illustrate our results.