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arXiv · 2505.00559

Evolution variational inequalities with general costs

Pierre-Cyril Aubin-Frankowski·Giacomo Enrico Sodini·Ulisse Stefanelli
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Abstract

We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions $c$, 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 $c$, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

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BibTeXRIS

Pierre-Cyril Aubin-Frankowski, Giacomo Enrico Sodini, Ulisse Stefanelli. 2026-03-30. Evolution variational inequalities with general costs. https://arxiv.org/abs/2505.00559

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