{"id":"https://openalex.org/W1628278711","doi":"https://doi.org/10.1137/140955483","title":"A Broyden Class of Quasi-Newton Methods for Riemannian Optimization","display_name":"A Broyden Class of Quasi-Newton Methods for Riemannian Optimization","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1628278711","doi":"https://doi.org/10.1137/140955483","mag":"1628278711"},"language":"en","primary_location":{"id":"doi:10.1137/140955483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955483","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016475334","display_name":"Wen Huang","orcid":"https://orcid.org/0000-0001-8324-2416"},"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":"Wen Huang","raw_affiliation_strings":["Department of Mathematical Engineering, ICTEAM Institute, Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, ICTEAM Institute, Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018426276","display_name":"Kyle A. Gallivan","orcid":"https://orcid.org/0000-0003-4572-4240"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. A. Gallivan","raw_affiliation_strings":["Department of Mathematics, 208 Love Building, 1017 Academic Way, Florida State University, Tallahassee FL 32306-4510, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, 208 Love Building, 1017 Academic Way, Florida State University, Tallahassee FL 32306-4510, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075495386","display_name":"Pierre-Antoine Absil","orcid":null},"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":["Department of Mathematical Engineering, ICTEAM Institute, Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, ICTEAM Institute, Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016475334"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":18.2378,"has_fulltext":false,"cited_by_count":184,"citation_normalized_percentile":{"value":0.9920394,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"25","issue":"3","first_page":"1660","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3398999869823456,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3398999869823456,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.274399995803833,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.10360000282526016,"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/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.8377578258514404},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8304648399353027},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.7127413153648376},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6273835301399231},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5989031791687012},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5133877992630005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47363534569740295},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4648163914680481},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.434086412191391},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.41297513246536255},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3855854570865631},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2825685739517212},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.133091002702713},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.09660670161247253},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07322698831558228}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.8377578258514404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8304648399353027},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.7127413153648376},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6273835301399231},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5989031791687012},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5133877992630005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47363534569740295},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4648163914680481},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.434086412191391},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.41297513246536255},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3855854570865631},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2825685739517212},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.133091002702713},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.09660670161247253},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07322698831558228},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140955483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955483","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:CiteSeerX.psu:10.1.1.722.3497","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.722.3497","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.fsu.edu/%7Ealuffi/archive/paper488.pdf","raw_type":"text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:160460","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/160460","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, Vol. 25, no. 3, p. 1660-1685 (2015)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W82623966","https://openalex.org/W1483866246","https://openalex.org/W1660706583","https://openalex.org/W1679203207","https://openalex.org/W1730255663","https://openalex.org/W1775030945","https://openalex.org/W1804110266","https://openalex.org/W1855068118","https://openalex.org/W1923779967","https://openalex.org/W1964176378","https://openalex.org/W1964650132","https://openalex.org/W1974766144","https://openalex.org/W1974824893","https://openalex.org/W2003809942","https://openalex.org/W2006571925","https://openalex.org/W2026245502","https://openalex.org/W2026892575","https://openalex.org/W2028324955","https://openalex.org/W2030405518","https://openalex.org/W2033793366","https://openalex.org/W2041285248","https://openalex.org/W2045968916","https://openalex.org/W2058078260","https://openalex.org/W2068484625","https://openalex.org/W2079354271","https://openalex.org/W2110662303","https://openalex.org/W2127567631","https://openalex.org/W2133323250","https://openalex.org/W2145179194","https://openalex.org/W2150386905","https://openalex.org/W2162211921","https://openalex.org/W2223029563","https://openalex.org/W2519358129","https://openalex.org/W2803512580","https://openalex.org/W2962777248","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W1628278711","https://openalex.org/W2555115694","https://openalex.org/W1616296999","https://openalex.org/W2546668543","https://openalex.org/W1532125927","https://openalex.org/W2059474323","https://openalex.org/W4302389195","https://openalex.org/W2952208990","https://openalex.org/W4304542716","https://openalex.org/W2107535157"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"and":[3,33,38],"analyzes":[4],"a":[5,19,25],"generalization":[6],"of":[7,11,17,51],"the":[8,15,49,52,55],"Broyden":[9,57],"class":[10,58],"quasi-Newton":[12],"methods":[13],"to":[14,54,66],"problem":[16],"minimizing":[18],"smooth":[20],"objective":[21],"function":[22],"$f$":[23],"on":[24,30,76],"Riemannian":[26,56,68],"manifold.":[27],"A":[28],"condition":[29],"vector":[31],"transport":[32],"retraction":[34],"that":[35,74],"guarantees":[36],"convergence":[37],"facilitates":[39],"efficient":[40],"computation":[41],"is":[42,46],"derived.":[43],"Experimental":[44],"evidence":[45],"presented":[47],"demonstrating":[48],"value":[50],"extension":[53],"through":[59],"superior":[60],"performance":[61],"for":[62],"some":[63],"problems":[64],"compared":[65],"existing":[67],"BFGS":[69],"methods,":[70],"in":[71],"particular":[72],"those":[73],"depend":[75],"differentiated":[77],"retraction.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":28},{"year":2020,"cited_by_count":30},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
