dc.contributor.author | Silva Louzeiro, Maurício | |
dc.contributor.author | Bergmann, Ronny | |
dc.contributor.author | Herzog, Roland | |
dc.date.accessioned | 2023-02-28T07:40:50Z | |
dc.date.available | 2023-02-28T07:40:50Z | |
dc.date.created | 2022-05-12T08:27:44Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | SIAM Journal on Optimization. 2022, 32 (2), 854-873. | en_US |
dc.identifier.issn | 1052-6234 | |
dc.identifier.uri | https://hdl.handle.net/11250/3054449 | |
dc.description.abstract | In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience that the conjugate depends on the choice of a certain point on the manifold, as previous definitions required. On the other hand, this new definition still possesses properties known to hold in the Euclidean case. It even yields a broader interpretation of the Fenchel conjugate in the Euclidean case itself. Most prominently, our definition of the Fenchel conjugate provides a Fenchel--Moreau theorem for geodesically convex, proper, lower semicontinuous functions. In addition, this framework allows us to develop a theory of separation of convex sets on Hadamard manifolds, and a strict separation theorem is obtained. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Fenchel Duality and a Separation Theorem on Hadamard Manifolds | en_US |
dc.title.alternative | Fenchel Duality and a Separation Theorem on Hadamard Manifolds | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | acceptedVersion | en_US |
dc.source.pagenumber | 854-873 | en_US |
dc.source.volume | 32 | en_US |
dc.source.journal | SIAM Journal on Optimization | en_US |
dc.source.issue | 2 | en_US |
dc.identifier.doi | 10.1137/21M1400699 | |
dc.identifier.cristin | 2023748 | |
cristin.ispublished | true | |
cristin.fulltext | preprint | |
cristin.qualitycode | 2 | |