{"id":"https://openalex.org/W3037966177","doi":"https://doi.org/10.1137/20m1348522","title":"Riemannian Optimization on the Symplectic Stiefel Manifold","display_name":"Riemannian Optimization on the Symplectic Stiefel Manifold","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3037966177","doi":"https://doi.org/10.1137/20m1348522","mag":"3037966177"},"language":"en","primary_location":{"id":"doi:10.1137/20m1348522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348522","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.15226","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028101406","display_name":"Bin Gao","orcid":"https://orcid.org/0000-0001-5290-4675"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bin Gao","raw_affiliation_strings":["ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101868996","display_name":"Nguyen Thanh Son","orcid":"https://orcid.org/0000-0001-6988-333X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen Thanh Son","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034347171","display_name":"P.-A. Absil","orcid":"https://orcid.org/0000-0003-2946-4178"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P.-A. Absil","raw_affiliation_strings":["ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070719742","display_name":"Tatjana Stykel","orcid":"https://orcid.org/0000-0002-6195-4268"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tatjana Stykel","raw_affiliation_strings":["Institute of Mathematics, University of Augsburg, Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Augsburg, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5028101406"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":3.7195,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92565947,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"31","issue":"2","first_page":"1546","last_page":"1575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9747999906539917,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.9109654426574707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8094404935836792},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.6070900559425354},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5045195817947388},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4542042911052704},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40584099292755127}],"concepts":[{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.9109654426574707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8094404935836792},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6070900559425354},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5045195817947388},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4542042911052704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40584099292755127},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1348522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348522","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.15226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.15226","pdf_url":"https://arxiv.org/pdf/2006.15226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:249366","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/249366","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, Vol. 31, no.2, p. 1546-1575 (2021)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:88857","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/88857","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.15226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.15226","pdf_url":"https://arxiv.org/pdf/2006.15226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2787453302","display_name":null,"funder_award_id":"30468160","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W273698207","https://openalex.org/W645520567","https://openalex.org/W1544770838","https://openalex.org/W1665592869","https://openalex.org/W1924859287","https://openalex.org/W1963794468","https://openalex.org/W1975099181","https://openalex.org/W2017415695","https://openalex.org/W2028324955","https://openalex.org/W2038181794","https://openalex.org/W2045512849","https://openalex.org/W2066911115","https://openalex.org/W2072931016","https://openalex.org/W2076605490","https://openalex.org/W2079354271","https://openalex.org/W2083961492","https://openalex.org/W2085173595","https://openalex.org/W2086285527","https://openalex.org/W2086953401","https://openalex.org/W2096089324","https://openalex.org/W2118075667","https://openalex.org/W2155597967","https://openalex.org/W2167137033","https://openalex.org/W2167623372","https://openalex.org/W2167928328","https://openalex.org/W2177394166","https://openalex.org/W2188921815","https://openalex.org/W2297679915","https://openalex.org/W2298597254","https://openalex.org/W2333041090","https://openalex.org/W2402588523","https://openalex.org/W2618148972","https://openalex.org/W2786627029","https://openalex.org/W2789764089","https://openalex.org/W2801805363","https://openalex.org/W2901545265","https://openalex.org/W2910524244","https://openalex.org/W2919784958","https://openalex.org/W3014571813","https://openalex.org/W3029645440","https://openalex.org/W3100659610","https://openalex.org/W3104984361","https://openalex.org/W4205293427","https://openalex.org/W4212894631","https://openalex.org/W4242766606","https://openalex.org/W4248776665","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W2187058597","https://openalex.org/W8105021","https://openalex.org/W1972361952","https://openalex.org/W4297967242","https://openalex.org/W4385970320","https://openalex.org/W2021613246","https://openalex.org/W2769537058","https://openalex.org/W4301808655","https://openalex.org/W2522170085","https://openalex.org/W2973399580"],"abstract_inverted_index":{"The":[0,59,133],"symplectic":[1,12,17,33,130],"Stiefel":[2,99],"manifold,":[3],"denoted":[4],"by":[5],"${Sp}(2p,2n)$,":[6,72],"is":[7,64,119],"the":[8,15,27,74,93,97,109,125,129,146,152,155],"set":[9,29],"of":[10,30,56,61,76,96,115,145,154],"linear":[11,50],"maps":[13],"between":[14],"standard":[16],"spaces":[18],"$\\mathbb{R}^{2p}$":[19],"and":[20,52,67,124],"$\\mathbb{R}^{2n}$.":[21],"When":[22],"$p=n$,":[23],"it":[24],"reduces":[25],"to":[26,65,92,103,139,142],"well-known":[28],"$2n\\times":[31],"2n$":[32],"matrices.":[34],"Optimization":[35],"problems":[36],"on":[37,71,89,121,128],"${Sp}(2p,2n)$":[38,90],"find":[39],"applications":[40],"in":[41],"various":[42],"areas,":[43],"such":[44],"as":[45],"optics,":[46],"quantum":[47],"physics,":[48],"numerical":[49],"algebra,":[51],"model":[53],"order":[54,102],"reduction":[55],"dynamical":[57],"systems.":[58],"purpose":[60],"this":[62],"paper":[63],"propose":[66],"analyze":[68],"gradient-descent":[69],"methods":[70],"where":[73],"notion":[75],"gradient":[77],"stems":[78],"from":[79],"a":[80,85,105],"Riemannian":[81,87],"metric.":[82],"We":[83],"consider":[84],"novel":[86],"metric":[88,95],"akin":[91],"canonical":[94],"(standard)":[98],"manifold.":[100],"In":[101],"perform":[104],"feasible":[106],"step":[107],"along":[108],"antigradient,":[110],"we":[111],"develop":[112],"two":[113],"types":[114],"search":[116],"strategies:":[117],"one":[118,127],"based":[120],"quasi-geodesic":[122],"curves":[123],"other":[126],"Cayley":[131],"transform.":[132],"resulting":[134],"optimization":[135],"algorithms":[136],"are":[137],"proved":[138],"converge":[140],"globally":[141],"critical":[143],"points":[144],"objective":[147],"function.":[148],"Numerical":[149],"experiments":[150],"illustrate":[151],"efficiency":[153],"proposed":[156],"methods.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}