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- Publisher Website: 10.1007/s10107-021-01673-8
- Scopus: eid_2-s2.0-85108108253
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Article: On linear optimization over Wasserstein balls
Title | On linear optimization over Wasserstein balls |
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Authors | |
Issue Date | 2021 |
Citation | Mathematical Programming, 2021 How to Cite? |
Abstract | Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under mild conditions, and we offer necessary and sufficient conditions for the existence of optimal solutions. We also characterize the sparsity of solutions if the Wasserstein ball is centred at a discrete reference measure. In comparison with the existing literature, which has proved similar results under different conditions, our proofs are self-contained and shorter, yet mathematically rigorous, and our necessary and sufficient conditions for the existence of optimal solutions are easily verifiable in practice. |
Persistent Identifier | http://hdl.handle.net/10722/313633 |
ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 1.982 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Yue, Man Chung | - |
dc.contributor.author | Kuhn, Daniel | - |
dc.contributor.author | Wiesemann, Wolfram | - |
dc.date.accessioned | 2022-06-23T01:18:49Z | - |
dc.date.available | 2022-06-23T01:18:49Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Mathematical Programming, 2021 | - |
dc.identifier.issn | 0025-5610 | - |
dc.identifier.uri | http://hdl.handle.net/10722/313633 | - |
dc.description.abstract | Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under mild conditions, and we offer necessary and sufficient conditions for the existence of optimal solutions. We also characterize the sparsity of solutions if the Wasserstein ball is centred at a discrete reference measure. In comparison with the existing literature, which has proved similar results under different conditions, our proofs are self-contained and shorter, yet mathematically rigorous, and our necessary and sufficient conditions for the existence of optimal solutions are easily verifiable in practice. | - |
dc.language | eng | - |
dc.relation.ispartof | Mathematical Programming | - |
dc.title | On linear optimization over Wasserstein balls | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10107-021-01673-8 | - |
dc.identifier.scopus | eid_2-s2.0-85108108253 | - |
dc.identifier.eissn | 1436-4646 | - |
dc.identifier.isi | WOS:000662825900001 | - |