Evolution variational inequalities with general costs
Functional Analysis
2026-03-31 v2 Metric Geometry
Abstract
We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions , including Bregman and entropic transport divergences. We establish several properties of the resulting flows, including stability and energy identities. Using novel notions of convexity related to costs , we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.
Keywords
Cite
@article{arxiv.2505.00559,
title = {Evolution variational inequalities with general costs},
author = {Pierre-Cyril Aubin-Frankowski and Giacomo Enrico Sodini and Ulisse Stefanelli},
journal= {arXiv preprint arXiv:2505.00559},
year = {2026}
}
Comments
34 pages