# Nonlinear and degenerate discounted approximation in discrete weak KAM theory

arXiv: https://arxiv.org/abs/2403.04563 · HTML: https://mlsanity.com/paper/2403.04563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2024.

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

- [MSR-Align: Policy-Grounded Multimodal Alignment for Safety-Aware Reasoning in Vision-Language Models](https://mlsanity.com/paper/2506.19257/) (2025)

## Abstract (arXiv)

In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator. We consider the associated vanishing discount problem with a non-degenerate condition and prove convergence of solutions as the discount factor goes to 0. We also discuss the uniqueness of the discounted solution. The convergence result is a selection principle for fixed points of a family of nonlinear operators.