Non-commutative Optimal Transport for semi-definite positive matrices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916139971379200 |
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| author | Gerolin, Augusto Monina, Nataliia |
| author_facet | Gerolin, Augusto Monina, Nataliia |
| contents | We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the existence of a minimizer, compute the weak dual formulation and prove $Γ$-convergence results, demonstrating convergence to both Unbalanced Non-commutative Optimal Transport (as the Entropy-regularization parameter tends to zero) and von Neumann entropy regularized Non-commutative Optimal Transport problems (as the unbalanced penalty parameter tends to infinity). To draw an analogy to the Non-commutative case, we provide a concise introduction of the static formulation of Unbalanced Optimal Transport between positive measures and bounded cost |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-commutative Optimal Transport for semi-definite positive matrices Gerolin, Augusto Monina, Nataliia Optimization and Control Functional Analysis We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the existence of a minimizer, compute the weak dual formulation and prove $Γ$-convergence results, demonstrating convergence to both Unbalanced Non-commutative Optimal Transport (as the Entropy-regularization parameter tends to zero) and von Neumann entropy regularized Non-commutative Optimal Transport problems (as the unbalanced penalty parameter tends to infinity). To draw an analogy to the Non-commutative case, we provide a concise introduction of the static formulation of Unbalanced Optimal Transport between positive measures and bounded cost |
| title | Non-commutative Optimal Transport for semi-definite positive matrices |
| topic | Optimization and Control Functional Analysis |
| url | https://arxiv.org/abs/2309.04846 |