Nonlinear and degenerate discounted approximation in discrete weak KAM theory
Optimization and Control
2024-03-08 v1
Abstract
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 . 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.
Cite
@article{arxiv.2403.04563,
title = {Nonlinear and degenerate discounted approximation in discrete weak KAM theory},
author = {Panrui Ni and Maxime Zavidovique},
journal= {arXiv preprint arXiv:2403.04563},
year = {2024}
}