Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909062444089344 |
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| author | Carlier, Guillaume Delalande, Alex Mérigot, Quentin |
| author_facet | Carlier, Guillaume Delalande, Alex Mérigot, Quentin |
| contents | We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative Stability of the Pushforward Operation by an Optimal Transport Map Carlier, Guillaume Delalande, Alex Mérigot, Quentin Optimization and Control We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain. |
| title | Quantitative Stability of the Pushforward Operation by an Optimal Transport Map |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.01088 |