Evolution variational inequalities with general costs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908919716118528 |
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| author | Aubin-Frankowski, Pierre-Cyril Sodini, Giacomo Enrico Stefanelli, Ulisse |
| author_facet | Aubin-Frankowski, Pierre-Cyril Sodini, Giacomo Enrico Stefanelli, Ulisse |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evolution variational inequalities with general costs Aubin-Frankowski, Pierre-Cyril Sodini, Giacomo Enrico Stefanelli, Ulisse Functional Analysis Metric Geometry 49J40, 37L05, 49J27, 49J52 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. |
| title | Evolution variational inequalities with general costs |
| topic | Functional Analysis Metric Geometry 49J40, 37L05, 49J27, 49J52 |
| url | https://arxiv.org/abs/2505.00559 |