A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917557416493056 |
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| author | Savaré, Giuseppe Sodini, Giacomo Enrico |
| author_facet | Savaré, Giuseppe Sodini, Giacomo Enrico |
| contents | We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_00542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation Savaré, Giuseppe Sodini, Giacomo Enrico Optimization and Control Functional Analysis Primary: 49Q22, 28A33, Secondary: 49K27 We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed. |
| title | A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation |
| topic | Optimization and Control Functional Analysis Primary: 49Q22, 28A33, Secondary: 49K27 |
| url | https://arxiv.org/abs/2401.00542 |